LCM ( Least Common Multiple)  : A Fun Learning Guide for Grade 4

LCM: What is it?

LCM simply means Least Common Multiple. It is the smallest number that happens to be a common multiple of two or more numbers.

 

 

How to find the LCM?

• Write the multiples of the numbers.

• Find the common multiples.

• Choose the least common multiple. 

Bingo! That's the LCM!

Example 1: Find the LCM of 4 and 5

• Multiples of 4: 4, 8, 12, 16, 20, 24, 28,.

• Multiples of 5: 5, 10, 15, 20, 25, 30,.

• The smallest common multiple is 20. Hence LCM(4, 5) = 20.

Example 2: Determine the LCM of 6 and 8

• Multiples of 6: 6, 12, 18, 24, 30, 36,.

• Multiples of 8: 8, 16, 24, 32, 40,.

The smallest common multiple is 24. Therefore, LCM(6, 8) = 24.

Prime factorization is breaking a number into prime factors, which are the smallest numbers that multiply to give the original number.

Find the LCM of 12 and 15 by using Prime Factorization

Prime Factorization of 12: 12 = 2 × 2 × 3

Prime factorization of 15: 15 = 3 × 5

Take all the prime factors, using the highest powers of each factor:

2, 2, 3, 5

Multiply the factors:

LCM = 2 x 2 x 3 x 5 = 60

 

LCM by Division Method

The Division Method

Involve in dividing the numbers by their common factors until no common factors are left.

Example: Find the LCM of 8 and 12 using the Division Method

Step 1: Divide by 2 (smallest prime number):

8 ÷ 2 = 4, 12 ÷ 2 = 6

New numbers: 4, 6

Step 2: Divide by 2 again:

4 ÷ 2 = 2, 6 ÷ 2 = 3

New numbers: 2, 3

Step 3. Divide again by 2 for 2 :

2 ÷ 2 = 1, 3 ÷ 2 doesn't work; divide now by 3 :

3 ÷ 3 = 1

New numbers: 1, 1

Multiply the factors:

LCM = 2 × 2 × 2 × 3 = 24

Interesting Fact about LCM:

•  

• Did you know that the LCM can help you when you’re scheduling events?
  For example, if two events happen at different times (like one every 4 days and another every 6 days), the LCM will tell you when both events will happen on the same day again!

• So, the LCM of 4 and 6 is 12, which means the two events will happen together every 12 days. Cool, right?

If you want to learn more click here

Quiz

1.What is the LCM of 6 and 9?

a) 18
b) 36
c) 54
d) 72

2. Find the LCM of 4 and 5.

a) 20
b) 40
c) 25
d) 10

3. What is the LCM of 8 and 12?

a) 24
b) 48
c) 36
d) 72

4. The LCM of two numbers is 60. One of the numbers is 12. What is the other number?

a) 24
b) 18
c) 15
d) 30

5. Which of the following pairs of numbers has an LCM of 18?

a) 3 and 6
b) 4 and 6
c) 2 and 9
d) 5 and 7

FAQs

How do you calculate LCM?

To calculate the LCM, list the multiples of the numbers, then find the smallest common multiple, or use prime factorization or the division method.

What is the LCM of 8 and 12?

The LCM of 8 and 12 is 24, as it is the smallest multiple both numbers share.

How to find LCM quickly?

You can find the LCM quickly by listing the multiples of each number and identifying the smallest common one or by using the prime factorization method.

What is the LCM rule?

The LCM rule states that the Least Common Multiple is the smallest number that is a multiple of each number in a given set.

 

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