What is the least common multiple of 14 and 21?

To find the least common multiple (LCM) of 14 and 21, we can first identify the prime factors of each number.

• The prime factorization of 14 is 2 × 7.

• The prime factorization of 21 is 3 × 7.

To determine the LCM, we take the highest power of each prime factor present in the factorizations:

• The prime number 2 appears with a maximum power of 1 (from 14).

• The prime number 3 appears with a maximum power of 1 (from 21).

• The prime number 7 appears with a maximum power of 1 (common to both).

Now, we multiply these together to find the LCM:

LCM = 2^1 × 3^1 × 7^1 = 2 × 3 × 7 = 42.

Thus, the least common multiple of 14 and 21 is indeed 42, making this the correct answer. The LCM represents the smallest number that both original numbers can divide into without leaving a remainder, confirming that 42 can evenly divide by both 14 and 21.