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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5th Grade Math Worksheet

Grade 5 students can try this free math worksheet to get touch with overall topics. Those who are new to 5th grade are advised to practice 4th grade math worksheet first then take this quiz next.

1.   Choose the greatest proper fraction from the following.

a.   12/7

b.   8/7

c.   4/7

d.   3/7

2.   Write the decimal form of 5/10.

a.   5

b.   2

c.   0.5

d.   0.05

3.   Write 25% as a fraction.

a.   1/4

b.   1/5

c.   1/6

d.   1/7

4.   Which of the following is not a factor of 9?

a.   1

b.   3

c.   6

d.   9

5.   ___ is neither prime nor composite

a.   Zero

b.   One

c.   Seven

d.   eleven

6.   Which of the following is a composite number?

a.   47

b.   37

c.   27

d.   17

7.   Lily solves eight questions from grade 5 math worksheets. But George solves seven times more questions than Lilly. Find the number of questions solved by George.

a.   32

b.   44

c.   48

d.   56

8.   Mrs. Miller’s family requires 54 gallons of milk for 9 days. How many gallons of milk required for each day?

a.   63

b.   45

c.   9

d.   6

9.   4(5+3)=________

a.   3+5

b.   5×3

c.   (4×5)+(4×3)

d.   (4+5)3

10. The simplest form of 14/49 is _______

a.   2/7

b.   7/24

c.   3/7

d.   3/24

11. Peter bought 16 balloons. Each balloon cost $0.50. Find the cost paid by peter for 16 balloons.

a.   $ 7

b.   $8

c.   $9

d.   $10

12. 24÷6+18=___________

a.   1

b.   14

c.   22

d.   30

13. Four less than a number is twenty.

 Write the above statement as an expression.

a.   4-n=20

b.   4n<20

c.   n-4=20

d.   n+4=20

14. If 5m=35, the value of m is ____

a.   40

b.     30

c.   15

d.   7

15.  

                                    

The given triangle is ________

a.   Isosceles triangle

b.   Straight triangle

c.   Equilateral triangle

d.   Scalene triangle

16.  

                                    

If O is the center and the line segment AB passes through the centre. Then AB is _______ of the circle.

a.   Radius

b.   Diameter

c.   Circumference

d.   Diagonal

17. Sum of the angles of a triangle is ________ degrees.

a.   90

b.   180

c.   270

d.   360

18. Find the perimeter of a given figure.

        

a.   28 m

b.   30 m

c.   35 m

d.   38 m

19. The perimeter of a square tank is 100 ft. Find the length of its side.

a.   10 m

b.   25 m

c.   50 m

d.   400 m

20.

                               

A spinner is given below. If you are spinning the spinner, find the probability of getting red color.

a.   1/8

b.   1/4

c.   1/3

d.   1/2

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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.

-----------------------------------------------------------------------------------

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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