What is the least common multiple (LCM) of the numbers 4 and 6?

What is the least common multiple (LCM) of the numbers 4 and 6?

• A. 8
• B. 12
• C. 24
• D. 36

Answer: (B)

To find the least common multiple (LCM) of two numbers, we look for the smallest multiple that both numbers share. The multiples of 4 are 4, 8, 12, 16, 20, 24, and so on. The multiples of 6 are 6, 12, 18, 24, and so on. By comparing these lists, we can see that the smallest common multiple is 12. Calculating it through another method also confirms this. The prime factorization of 4 is \(2^2\) and for 6, it's \(2^1 \times 3^1\). To find the LCM, we take the highest power of each prime that appears in the factorization of the numbers. Thus, we take \(2^2\) from 4 and \(3^1\) from 6, resulting in \(2^2 \times 3^1 = 4 \times 3 = 12\). Therefore, the least common multiple of 4 and 6 is indeed 12.

To find the least common multiple (LCM) of two numbers, we look for the smallest multiple that both numbers share. The multiples of 4 are 4, 8, 12, 16, 20, 24, and so on. The multiples of 6 are 6, 12, 18, 24, and so on. By comparing these lists, we can see that the smallest common multiple is 12.

Calculating it through another method also confirms this. The prime factorization of 4 is (2^2) and for 6, it's (2^1 \times 3^1). To find the LCM, we take the highest power of each prime that appears in the factorization of the numbers. Thus, we take (2^2) from 4 and (3^1) from 6, resulting in (2^2 \times 3^1 = 4 \times 3 = 12).

Therefore, the least common multiple of 4 and 6 is indeed 12.