Question

Find the LCM of 24, 36, and 62

Answer 1

The LCM is the smallest number that is a multiple of the given numbers.

To find it we can make a list of the multiples for each number until we find the smallest multiple they have in common, also we can find the prime factorization for each number first:

Prime factorization for 62:

`31*2\text{ (31 is a prime number)}`

Prime factorization for 36:

`4*9=2*2*3*3=2^2*3^2`

Prime factorization for 24:

`6*4=3*2*2*2=3*2^3`

For each prime factor, let's find where it occurs most often as a factor and write it that many times in a new list:

New list: 31, 3, 2: 31 occurs one time, 3 occurs most often two times in the prime factorization for 36, and 2 occurs most often three times in the prime factorization for 24, then the LCM is:

`31*3^2*2^3=31*3*3*2*2*2=2232`

Answer: The LCM of 24, 36 and 62 is 2232