Find the LCM by factoring.
-8, 24, 15
A)360
B)24
C)120
D)2880

Question

Quizplus · Accepted Answer

First, we need to factor each number into its prime factors:
8 = 2 x 2 x 2
24 = 2 x 2 x 2 x 3
15 = 3 x 5

Next, we take the highest power of each prime factor that appears in any of the numbers. In this case, we need 2 cubed (highest power of 2 that appears), 3 (highest power of 3 that appears), and 5 (highest power of 5 that appears). Multiplying these together, we get:

2^3 x 3 x 5 = 120

Therefore, 120 is the LCM. Choice C is the correct answer. Step 1: Prime factorize each number
8 = 2^3
24 = 2^3 * 3^1
15 = 3^1 * 5^1

Step 2: Write down the prime factors with the highest exponent from each number
2^3 * 3^1 * 5^1

Step 3: Multiply the prime factors together
2^3 * 3^1 * 5^1 = 120

Therefore, the LCM of 8, 24, and 15 is 120. Answer choice C (120) is the best choice.

Find the LCM by Factoring