Find the least common multiple (LCM)of the list of numbers.
-24, 54, 3
A)108
B)54
C)216
D)72

Question

Quizplus · Accepted Answer

We can find the LCM by finding the prime factorization of each number and then taking the product of the highest powers of each prime factor.

24 = 2^3 * 3 
54 = 2 * 3^3 
3 = 3

The highest power of 2 is 2^3, the highest power of 3 is 3^3, and we also have a factor of 3^1. Taking the product of these, we get:

LCM = 2^3 * 3^3 = 216

Therefore, the answer is C. The prime factorization of 24 is 2^3*3^1.
The prime factorization of 54 is 2^1*3^3.
The prime factorization of 3 is 3^1.
To find the LCM, we need to take the highest power of each prime factor, which gives us:
2^3 * 3^3 = 216
Therefore, the LCM is 216, which is choice C.

Find the Least Common Multiple (LCM)of the List of Numbers