HOW TO FIND THE LEAST COMMON MULTIPLE OF PRIME NUMBERS

What is least common multiple?

Least common multiple is the smallest number which is a multiple of the given numbers.

Let us list out the positive integers which are the common multiples of 2 and 3.

6, 12, 18, 24, ............

In the above list, 6 is the first positive integer which is being a common multiple of 2 and 3.

Is there any positive integer less than 6 which is a common multiple of 2 and 3.

The answer is NO.

6 is the smallest positive integer which is a common multiple of 2 and 3.

Therefore, 6 is the least common multiple of 2 and 3.

In each case, find the least common multiple of the given numbers.

Example 1 :

3 and 5

Solution :

The numbers 3 and 5 are prime numbers.

Therefore, the least common multiple of 3 and 5 is

= 3 x 5

= 15

Example 2 :

5 and 7

Solution :

The numbers 5 and 7 are prime numbers.

Therefore, the least common multiple of 5 and 7 is

= 5 x 7

= 35

Example 3 :

11 and 13

Solution :

The numbers 11 and 13 are prime numbers.

Therefore, the least common multiple of 11 and 13 is

= 11 x 13

= 143

Example 4 :

17 and 19

Solution :

The numbers 17 and 19 are prime numbers.

Therefore, the least common multiple of 17 and 19 is

= 17 x 19

= 323

Example 5 :

23 and 29

Solution :

The numbers 23 and 29 are prime numbers.

Therefore, the least common multiple of 23 and 29 is

= 23 x 29

= 667

Example 6 :

2, 3 and 5

Solution :

The numbers 2, 3 and 5 are prime numbers.

Therefore, the least common multiple of 2, 3 and 5 is

= 2 x 3 x 5

= 30

Example 7 :

5, 7, 11 and 13

Solution :

The numbers 5, 7, 11 and 13 are prime numbers.

Therefore, the least common multiple of 5, 7, 11 and 13 is

= 5 x 7 x 11 x 13

= 5005

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