LCM: Least Common Multiple Worksheets

This tutorial explains how to find the least common multiple (some people say lowest common multiple) of any two or three given numbers with detailed example. LCM worksheets provided at the end of tutorial to practice.

LCM for any two numbers:

Least common multiple (LCM) for any given numbers is a lowest number which is divisible by all the numbers taken into account. Not clear??? Look at the following example.

Take any two numbers say 3 and 5. Now list the numbers that are divisible by both 3 and 5. We have 15, 30, 45, 60 and so on. Among those numbers which is smallest? Yes, you are right, it is 15. So, we can say that 15 is the lowest common multiple of 3 and 5. It is easy to find LCM for smaller numbers. Let us see how to find LCM for bigger numbers. Here is an example.

Find the LCM of 24 and 36:

It is really hard for anyone to find the number which is divisible by both 24 and 36. We are going to use the following trick to make it easy.

Use prime factor tree method to split numbers into product of primes.

Taking only the primes, we can write 24 and 36 as below.

24 = 2 * 2 * 2 * 3

36 = 2 * 2 * 3 * 3

Take common primes once and then take uncommon primes as below:

LCM = 2 * 2 * 3 * 2 * 3 = 72

72 is the least number which is divisible by both 24 and 36. Therefore 72 is the Least Common Multiple of 24 and 36.

LCM worksheets: Level 1

Find the least common multiple for the following pair of numbers.

a) 5, 7

b) 8, 9

c) 12, 15

d) 36, 48

e) 72, 96

LCM for any three numbers:

Procedure for finding least common multiple of any three numbers is not any more different that explained for two numbers. Anyway, here is an example for clear understanding.

Find the LCM of 12, 18 and 24:

Prime factorize 12, 18 and 24 using prime factor tree method.

What is our next step? Not sure? Refer previous example. Yes, you are right. We have to take common primes for all three numbers, then take common primes for any two numbers and then finally take all primes which is not yet considered.

Circled with blue and red repeats in all three numbers. So, take it just once. We have 2 * 3.

Circled with green repeats in two places. Taking that once along with previous common factors, we have 2 * 3 * 2.

Look at the orange circle which never repeats in any places after picking all common primes.

Choosing them, we have 2 * 3 * 2 * 3 * 2.

Finally, we can say, LCM of 12, 18 and 24 = 2 * 3 * 2 * 3 * 2 = 72.

LCM worksheets: Level 2

What is the least common multiple for the given numbers?

a) 5, 7, 8

b) 8, 16, 32

c) 4, 12, 16

d) 24, 36, 42

e) 48, 56, 72

Few easy ways to find LCM:

1) If any two distinct numbers are prime, then LCM is product of those numbers.

For example, let’s take two prime numbers 5 and 7. LCM of 5 and 7 = 5 * 7 = 35

It works with any number of unique prime numbers.

Can you try the LCM of 5, 7 and 11?

LCM worksheets: Type 1

Find the lowest common multiple of the following.

a) 2, 3

b) 2, 3, 5

c) 7, 11

d) 11, 13

e) 3, 7

2) Are you familiar with Co-primes? Here is an example. Is 4 a prime? No. Is 9 a prime? No.

But 4 and 9 are co-prime. Have any guess why they are co-prime? I think you got the point. There are no common factors for 4 and 9. So, 4 and 9 are co-prime. LCM of co-prime numbers is just a product of those numbers. Do you understand this? What is the least common multiple for 4 and 9? Yes, you are right. It is just a product of 4 and 9. LCM of 4 and 9 = 4 * 9 = 36.

What is the LCM of 4, 9 and 25? Try it yourself.

What is the LCM of 3 and 4? Here 3 is prime, 4 is composite but both 3 and 4 are co-prime as it doesn’t contain common factors. So, LCM of 3 and 4 = 3 * 4 = 12

LCM worksheets: Type 2

Find the least common multiple for the given numbers:

a) 2, 9

b) 5, 6

c) 7, 8

d) 8, 11

e) 6, 11, 13

3) Now let’s take a number 4 and 8. What you can say about these numbers? 4 divides 8, isn’t it?

Therefore, LCM of 4 and 8 is just 8 itself. What is the LCM of 8 and 16? Yes, you are right. It is 16.

LCM worksheets: Type 3

Find the least common multiple of the following:

a) 5, 25

b) 2, 4, 8

c) 3, 9, 18

d) 6, 12

e) 14, 42

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Addition and Subtraction Word Problems

Each example with complete solution for addition and subtraction word problems is given. Practice with example questions and try unsolved word problems.

Addition Word Problems:

1.   There are twelve red marbles, twenty-four yellow marbles and seventeen green marbles in a box. Find the total number of marbles.

Solution:

Number of red marbles       =    12

Number of yellow marbles =    24

Number of green marbles   =  +17

Total number of marbles     =  53

2.   Andrew counted the number of visitors in his shop. There are 134 males 123 females. Find the total number of visitors in the shop.

3.   In a garden, there are twenty-two guavas, eleven pine apples and fourteen bananas. Find the total number of fruits in the garden.

4.   Morgan bought crayons for $12.50, painting brush for $3.25 and drawing books for $ 18. Find the total of the bill.

5.   Watson collected 12 Canadian stamps, 13 American stamps and 11 Indian stamps. Find the total stamps collected by Watson.

6.   Edward Schools arranges for a camp. There are 39 girls and 43 boys in the camp. Find the total number of students in the camp.

7.   Adam bought lollipops for $ 5.75, brownies for $ 6.75 and cakes for $ 23. Find the money Adam spent in total.

8.   The test scores of Shady are given below:

English =78, Math = 89 and Science = 71.

Find the total score of Shady.

Subtraction Word Problems:

9.   Laura, teacher of grade 3 students has 84 gifts for her students. There are 67 students and each received one gift from the teacher. Find the number of gifts remaining with Laura.

Solution:

Total number of gifts with Laura            =   84

Number of gifts distributed to students= - 67

Number of gifts left with Laura                = 14

10.   Emily bought 42 tomatoes and out of them 27 was rotten. Find the number of good ones.

11.   Cooper had $ 126 in his savings. He has $78 after spending for a video game. Find the amount left in his savings.

12.   Sara had 34 stickers and she gave 16 of it to her friend. Find the number stickers left with Sara.

13.   Santa brought 89 gifts and distributed 65 gifts for the Christmas Eve. Find the number of gifts left with Santa.

14.   Hudson needs seven hundred seventy dollars to buy a digital camera. But he has seven hundred and eleven dollars with him. How much money did he need to buy the camera?

15.   There are 679 books in Martin’s library. If there are 389 books are biographies, find the other number of books in the library.

16.   Josephina received 235 dollars from her mother. She spent 126.75 dollars for stationary items. Find the amount left with Josephina.

After trying above questions, take this mixed quiz which contains word problems involving both addition and subtraction.

Mixed Problems:

17.   Bailey has to solve 125 Math problems. She solved 46 problems yesterday and 53 problems today. How many problems yet to solve?

18.   Rose arranges a small party for her eleventh birth day with an amount of $150. She spends. She bought cola for $12.50, cake for $80, cookies for $ 24 and French fries for $14. Find the balance amount of Rose.

19.   Jefferson purchased pens for $ 56 and pencils for $34. He gave $ 100 for the bill. How much will he get back as change?

20.   Jenny earned $ 2500 in April from her company project. She spent $ 345 for entertainment and $ 600 on rent and the remaining she maintained for savings. Find the amount she saved for the month of April.

21.   Kevin received 150 dollars from his mother and 200 dollars from his father and he spent 195 on entertainment. Find the amount left with Kevin.

22.   Britney earned a profit of $300 from sales company and $ 400 from small business. If she spends $90 on theatre $ 350 on cosmetics, find the amount left with Britney.

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4th Grade Math Worksheet

This free math worksheet contains practice questions for grade 4 students. Keystage 1 students can also practice this question paper.

1.   Find the place value of 9 in 348.719.

a.   9 hundredths

b.   9 thousandths

c.   9 hundreds

d.   9 thousands

2.   Which is the greatest 2 digit prime number?

a.   99

b.   97

c.   91

d.   83

3.   30 cents+2 dimes=________

a.   2 quarters

b.   4 nickels

c.   10 dimes

d.   100 cents

4.   The Math test scores of Grade 4 students are given below:

90, 56, 36, 55, 99, 55, 67, 42, 51, 63 and 65.

Find the range of the above data.

a.   99

b.   36

c.   63

d.   55

5.   A shelf contains 7 boxes. There are 12 pencils in a box. How many pencils are there in total?

a.   19

b.   5

c.   84

d.   14

6.   Estimate the area of a picture in the given grid:

     

a.   18 sq. units

b.   14 sq. units

c.   12 sq. units

d.   8 sq. units

7.   5 ft 3 in + 2 ft 5 in is equal to ______

a.   7 ft 8 in

b.   8 ft 7 in

c.   3 ft 2 in

d.   0 ft 2 in

8.   2 cm=___ mm

a.   10

b.   20

c.   100

d.   200

9.   There are 8000 grams of rice in a container. Dawn wanted to make 1 kg of rice in each bag. How many bags are required to empty the container?

a.   8000

b.   800

c.   80

d.   8

10. 

       

The given triangle is _________

a.   Equilateral triangle

b.   Isosceles triangle

c.   Right triangle

d.   Scalene triangle

11.  In a rectangle, which of the following statement is not true?

a.   Sides are equal

b.   The angles are 90 degree

c.   Diagonals bisect each other

d.   Diagonals are equal

12. If a ray makes an angle 50 degree with a straight line, the angle formed is _____

a.   Acute angle

b.   Obtuse angle

c.   Right angle

d.   Straight angle

13. 

            

The given triangle is ________triangle

a.   Acute

b.   Obtuse

c.   Right

d.   Straight

14. Fill in the missing number in the given number sequence:

1, 4, 10, 13, 16, ___, 22, 25.

a.   17

b.   18

c.   19

d.   20

15. Choose the correct expression for the given statement:

Cathy has n number of apples. He gave away 3 of the apples to his friend.

a.   n+3

b.   3n

c.   n-3

d.   3

16. Jason filled 6 cups of water in the first can. 12 cups of water in the second can and 18 cups of water in the third can. If the pattern continues, which can is filled with 36 cups of water?

a.     4

b.   5

c.   6

d.   7

17.  If y=3+x and x takes the value as 4, then the value of y is ______

a.   7

b.   6

c.   5

d.   4

18.There are 5 green color beads and 6 yellow color beads in a box. Find the probability of selecting a green bead from the box.

a.   5/6

b.   1/11

c.   6/5

d.   1/5

19. Find the median for the given data:

45, 22, 76, 90, 35, 78,92

a.   45

b.   76

c.   78

d.   90

20. The bar graph given below shows the Math scores of grade 4 classmates. Who is in the second highest position?

    

a.   Jack

b.   Tony

c.   Lara

d.   Eric

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>> Fraction Word Problems

Fraction Word Problems

Fraction word problems for addition and subtraction is given here. This fraction word problems worksheet contains both proper and improper fractions. Student needs to be be really careful in understanding the real world situation of fraction word problems, needs to be cautious where to apply addition and subtraction.

Printable questions and answers for fraction word problems is given below. Student can download this fraction worksheet for free.

1)Stewart won 50 ¹/₅ dollars and Edward won 30 ²/₅ dollars in a race. What was the total cash price of the race?

Solution:

To find total amount, add 50 ¹/₅ and 30 ²/₅.

Here the denominators are equal.

50 ¹/₅ + 30 ²/₅ = 80 ³/₅.

Total cash prize = 80 ³/₅ dollars.

2) Mr. Mark’s family went for a trip. To make the journey interesting, they travelled first 53 ¹/₄ km by car and the remaining 10 ²/₃ km by horse ride. What was the total distance of the trip?

Solution:

To find the total distance, add 53 ¹/₄ and 10 ²/₃.

Let us convert the given mixed fractions into improper fractions.

53 ¹/₄= ²¹³/₄ and 10 ²/₃ = ³²/₃.

Here the denominators are unequal.

To make the denominators equal, we have to find the L.C.M of 3 and 4.

Multiples of 3= 3, 6, 9, 12 ….

Multiples of 4= 4, 8, 12, 16 ….

L.C.M= 12

To find common denominator, multiply both numerator and denominator of ²¹³/₄ by 3 and ³²/₃ by 4.

²¹³/₄ = ⁶³⁹/₁₂ ; ³²/₃ = ¹²⁸/₁₂

Now, ⁶³⁹/₁₂+ ¹²⁸/₁₂ = ⁷⁶⁷/₁₂ km = 63 ¹¹/₁₂ km

Total distance and covered = 63 ¹¹/₁₂ km.

3) Mr. White and Co. has total profit of ⁶/₇ of million dollars. The spinning department gave a profit of ¹/₂ of million dollars and weaving department gave a profit of ¹/₄ of million dollars. Find the fraction of profit from other departments.

Solution:

Total profit =⁶/₇

Profit from spinning and weaving departments=¹/₂ +¹/₄

Profit from other departments =⁶/₇-(¹/₂+¹/₄)

Here to make the denominators equal we have to find the L.C.M of 7, 2 and 4.

Multiples of 7= 7, 14, 21, 28 ….

Multiples of 2= 2, 4, 6, 8, 12, …, 26, 28 …

Multiples of 4= 4, 8, 12, 16, 20, 24, 28 …

L.C.M= 28.

⁶/₇= ^6*4/_7*4 = ²⁴/₂₈ (To make the denominator 28, multiply and divide by 4).

¹/₂= ^1*14/_2*14 =¹⁴/₂₈ (To make the denominator 28, multiply and divide by 14).

¹/₄=^1*7/_4*7 =⁷/₂₈ (To make the denominator 28, multiply and divide by 7).

Profit from other departments = ²⁴/₂₈-(¹⁴/₂₈+⁷/₂₈)

= ²⁴/₂₈ - ²¹/₂₈

= ³/₂₈

Therefore profit from other departments= ³/₂₈ of million dollars.

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Fraction Word Problems Worksheet:

i) Three friends Christ, Marx and Davey participated in gun shooting events. Each of them was given 10 chances. They hit the targets 3 times, 2 times and 4 times respectively out of 10 chances each. Find the total targets hit by them in fraction.

ii) An side of an equilateral triangle is ³/₁₁ feet. Find the perimeter of a triangle.

iii) The length and width of a rectangle is ³/₂ cm and ¹/₂ cm respectively. Find the perimeter of a rectangle.

iv) Sam celebrates his birthday with two small cakes. 7 people attended the birthday party. What fraction of cake each one will receive excluding Sam?

v) Nick and Robert have worked together and completed ³/₄ of work in a day. Robert has done ²/₅ of work. Find the work done by Nick.

vi) Mr. Briar, principal of Edward Public School, collects funds for School development. ²/₃ of funds are collected from school students and ¹/₆ of funds are collected from school development charity and the rest are collected from Public. What fraction of funds collected from public?

vii) Anne has 1 pizza, Eris ton has 1 ³/₄ of pizza and Julie has ¹/₇ of pizza. Find the total number of pizzas.

viii) To make a milk shake, 2 gallons of milk, ¹/₇ of gallons of essence and ³/₄ of gallons of fruit juice were required. Find the total gallons of milk shake made out of it.

ix) Harris has to travel 2 ²/₃ of a mile. He walked 1 ¹/₃ of the distance and the remaining by car. Find the distance covered by car.

x) Kate and Tony took part in running race. They covered a distance of ⁵/₈ yards and ⁸/₉ yards respectively. Find the distance between these athletes.
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