LEAST COMMON MULTIPLE OF RELATIVELY PRIME NUMBERS

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

Example 1 :

2 and 3

Solution :

There is no common divisor for 2 and 3 other than 1.

So, 2 and 3 are relatively prime.

Therefore, the least common multiple of 2 and 3 is

= 2 x 3

= 6

Example 2 :

4 and 5

Solution :

There is no common divisor for 4 and 5 other than 1.

So, 4 and 5 are relatively prime.

Therefore, the least common multiple of 4 and 5 is

= 4 x 5

= 20

Example 3 :

8 and 15

Solution :

Resolve 8 and 15 into their prime factors.

8 = 2 x 2 x 2

15 = 3 x 5

There is no common factor or divisor for 8 and 15 other than 1.

So, 8 and 15 are relatively prime.

Therefore, the least common multiple of 8 and 15 is

= 8 x 15

= 120

Example 4 :

4, 15, and 49

Solution :

Resolve 4, 15, and 49 into their prime factors.

4 = 2 x 2

15 = 3 x 5

49 = 7 x 7

There is no common factor or divisor for 4, 15 and 49 other than 1.

So, 4, 15 and 49 are relatively prime.

Therefore, the least common multiple of 4, 15 and 49 is

= 4 x 15 x 49

= 2940

Example 5 :

8, 15, and 77 

Solution :

Resolve 8, 15, and 77 into their prime factors.

8 = 2 x 2 x 2

15 = 3 x 5

77 = 7 x 11

There is no common factor or divisor for 8, 15 and 77 other than 1.

So, 8, 15 and 77 are relatively prime.

Therefore, the least common multiple of 8, 15 and 77 is

= 8 x 15 x 77

= 9240

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