In each case, find the least common multiple of the given numbers.
Problem 1 :
2 and 3
Problem 2 :
4 and 5
Problem 3 :
8 and 15
Problem 4 :
4, 15, and 49
Problem 5 :
8, 15, and 77
1. Answer :
2 and 3
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
Note :
To find the least common multiple of relatively prime numbers, we have to multiply them and the product is the least common multiple.
2. Answer :
4 and 5
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
3. Answer :
8 and 15
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
4. Answer :
4, 15, and 49
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
5. Answer :
8, 15, and 77
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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