What is the least common multiple of two numbers?

What is the least common multiple of two numbers?

• A. The sum of two numbers
• B. The maximum of two numbers
• C. The product of two values
• D. The smallest value common multiple of two values

Answer: (D)

The least common multiple is the smallest positive number that is a multiple of both numbers. In other words, it’s the smallest value that both numbers can divide into evenly. That’s why the description “the smallest value common multiple of two values” is the correct one. For example, with 6 and 8, the multiples are: - 6: 6, 12, 18, 24, ... - 8: 8, 16, 24, ... The first number that appears in both lists is 24, so 24 is the least common multiple. The product, 48, is also a common multiple but not the smallest. If the numbers are relatively prime, the least common multiple happens to equal the product, but in general it’s smaller than the product. So the essential idea is that the least common multiple is the smallest shared multiple, not a sum, not the larger of the two numbers, and not necessarily the product.

The least common multiple is the smallest positive number that is a multiple of both numbers. In other words, it’s the smallest value that both numbers can divide into evenly. That’s why the description “the smallest value common multiple of two values” is the correct one.

For example, with 6 and 8, the multiples are:

• 6: 6, 12, 18, 24, ...

• 8: 8, 16, 24, ...

The first number that appears in both lists is 24, so 24 is the least common multiple. The product, 48, is also a common multiple but not the smallest. If the numbers are relatively prime, the least common multiple happens to equal the product, but in general it’s smaller than the product.

So the essential idea is that the least common multiple is the smallest shared multiple, not a sum, not the larger of the two numbers, and not necessarily the product.