Math  /  Numbers & Operations

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What is the least common multiple of 4,6 , and 8 ?

Studdy Solution

STEP 1

1. We are finding the least common multiple (LCM) of the numbers 4, 6, and 8.
2. The LCM is the smallest positive integer that is divisible by each of the numbers.

STEP 2

1. List the prime factors of each number.
2. Determine the highest power of each prime number that appears in the factorizations.
3. Calculate the LCM by multiplying these highest powers together.

STEP 3

List the prime factors of each number:
- 4=224 = 2^2 - 6=21×316 = 2^1 \times 3^1 - 8=238 = 2^3

STEP 4

Identify the highest power of each prime that appears in the factorizations:
- The highest power of 22 is 232^3 (from 8). - The highest power of 33 is 313^1 (from 6).

STEP 5

Calculate the LCM by multiplying these highest powers together:
LCM=23×31=8×3=24\text{LCM} = 2^3 \times 3^1 = 8 \times 3 = 24
The least common multiple of 4, 6, and 8 is:
24\boxed{24}

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