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

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To determine the least common multiple (LCM) of two numbers, you can use the method of listing the multiples of each number or by finding the prime factorization.

For the numbers 4 and 6, we first identify their multiples:

• The multiples of 4 are: 4, 8, 12, 16, 20, 24, ...

• The multiples of 6 are: 6, 12, 18, 24, 30, ...

The LCM is the smallest multiple that appears in both lists. From the lists above, the first common multiple is 12. Therefore, the least common multiple of 4 and 6 is 12.

Alternatively, using prime factorization:

• The prime factorization of 4 is (2^2).

• The prime factorization of 6 is (2^1 \times 3^1).

To find the LCM using prime factors, you take the highest power of each prime number that appears in the factorizations. For 2, the highest power is (2^2) (from 4), and for 3, it is (3^1) (from 6). Thus,