Find the least common multiple of 18, 28, and 48.
A)2
B)24,192
C)1,008
D)42

Question

Quizplus · Accepted Answer

First, we can find the prime factorizations of each number: 
18 = 2 * 3^2
28 = 2^2 * 7
48 = 2^4 * 3
To find the LCM, we need to take the highest power of each prime factor that appears in any of the numbers. 
The highest power of 2 is 2^4
The highest power of 3 is 3^2
The highest power of 7 is 7^1
Therefore, LCM = 2^4 * 3^2 * 7^1 = 1,008. 
So the best choice is C. Prime factorizing the given numbers, we get:
18 = 2 x 3²
28 = 2² x 7
48 = 2⁴ x 3
The LCM should have all the factors with the highest powers present in the given numbers, which are 2⁴, 3², and 7. Multiplying these, we get:
LCM = 2⁴ x 3² x 7 = 1,008, which is the least common multiple of 18, 28, and 48. Therefore, the answer is C.

Find the Least Common Multiple of 18, 28, and 48