Two numbers are considered to be relatively prime or coprime, if there is no common divisor for those two numbers other than 1.
To find the least common multiple of relatively prime numbers, we have to multiply them.
For example, there is no common divisor for 4 and 7 other than 1. So, 4 and 7 are relatively prime numbers and its least common multiple is
= 4 x 7
= 28
In the same way, we can find the least common multiple of more than two numbers which are relatively prime.
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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