Question

The LCM of three numbers is 48. What are the numbers?

2, 3, 4
6, 16, 24
3, 8, 12
6, 8, 12

Answer 1

{6, 16, 24}

Explanation:

The least common multiple is the least number that is common to the multiples of two or more numbers.

The LCM of 2,3,4 is 12

The LCM of 6,16,and 24 is 48

The LCM of 3,8, 12 is 24.

The LCM of 6,8, 12 is 24.

The numbers that have the least common multiple of 48 is {6, 16, 24}

`6=2* 3`

`16=2^4`

`24=2^3* 3`

The LCM is the product of the highest powers of the common factors

`2^4*3=48`