Which is the smallest multiple that two numbers have in common?

Which is the smallest multiple that two numbers have in common?

• A. Greatest Common Factor
• B. Common Factor
• C. Least Common Multiple
• D. Difference

Answer: (C)

The main idea here is the least common multiple—the smallest positive integer that is a multiple of both numbers. To see why this is the correct idea, imagine listing multiples of each number and looking for the first number that appears in both lists. For example, multiples of 4 are 4, 8, 12, 16, … and multiples of 6 are 6, 12, 18, … The first common value is 12, so 12 is the smallest number that both numbers can multiply into. This is different from the greatest common factor, which is the largest number that divides both numbers without a remainder, or from a common factor, which is any number that divides both numbers (not necessarily a multiple). The difference between the two numbers is unrelated to finding a common multiple.

The main idea here is the least common multiple—the smallest positive integer that is a multiple of both numbers. To see why this is the correct idea, imagine listing multiples of each number and looking for the first number that appears in both lists. For example, multiples of 4 are 4, 8, 12, 16, … and multiples of 6 are 6, 12, 18, … The first common value is 12, so 12 is the smallest number that both numbers can multiply into.

This is different from the greatest common factor, which is the largest number that divides both numbers without a remainder, or from a common factor, which is any number that divides both numbers (not necessarily a multiple). The difference between the two numbers is unrelated to finding a common multiple.