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Math  /  Numbers & Operations

QuestionWhat is the least common multiple of 12 and 52?52 ? 624 156 112 312

Studdy Solution

STEP 1

1. We need to find the least common multiple (LCM) of the numbers 12 12 and 52 52 .
2. The LCM is the smallest positive integer that is divisible by both numbers.
3. We will use the prime factorization method to find the LCM.

STEP 2

1. Find the prime factorization of each number.
2. Identify the highest power of each prime number from the factorizations.
3. Calculate the LCM by multiplying these highest powers together.

STEP 3

Find the prime factorization of 12 12 .
12=22×31 12 = 2^2 \times 3^1

STEP 4

Find the prime factorization of 52 52 .
52=22×131 52 = 2^2 \times 13^1

STEP 5

Identify the highest power of each prime number from the factorizations.
- For prime number 2 2 , the highest power is 22 2^2 . - For prime number 3 3 , the highest power is 31 3^1 . - For prime number 13 13 , the highest power is 131 13^1 .

STEP 6

Calculate the LCM by multiplying these highest powers together.
LCM=22×31×131 \text{LCM} = 2^2 \times 3^1 \times 13^1

STEP 7

Perform the multiplication.
LCM=4×3×13=12×13=156 \text{LCM} = 4 \times 3 \times 13 = 12 \times 13 = 156
The least common multiple of 12 12 and 52 52 is:
156\boxed{156}

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