What is the least common multiple (LCM) of 12 and 18? — GMAT

What is the least common multiple (LCM) of $12$ and $18$ ?

Cevap: 36

The least common multiple of

12

and

18

36

To find the least common multiple of

12

and

18

, determine the prime factorization of each number (

12 = 2^2 \times 3^1

and

18 = 2^1 \times 3^2

). The LCM is calculated by taking the maximum power of each prime factor present:

2^2 \times 3^2 = 4 \times 9 = 36

Express both numbers in terms of their prime factorizations.

12 = 2^2 \times 3^1

and

18 = 2^1 \times 3^2

Prime factorization separates each number into basic prime components.

Select the highest power of each prime factor that appears in either factorization.

The highest power of

2

2^2

, and the highest power of

3

3^2

The least common multiple must contain enough factors to be divisible by both original numbers.

Calculate the product of these highest prime powers.

\text{LCM}(12, 18) = 2^2 \times 3^2 = 4 \times 9 = 36

Multiplying the chosen powers yields the minimum integer divisible by both

12

and

18

Finding the Least Common Multiple (LCM) via Prime Factorization

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