Which number is a multiple of both 4 and 6?

Which number is a multiple of both 4 and 6?

• A. 12
• B. 8
• C. 14
• D. 18

Answer: (A)

A number that is a multiple of both 4 and 6 is a common multiple of those two numbers. To find one, think of multiples of each: multiples of 4 are 4, 8, 12, 16, 20, … and multiples of 6 are 6, 12, 18, 24, …. The first number that appears in both lists is 12, so 12 is divisible by 4 and by 6 (12 ÷ 4 = 3 and 12 ÷ 6 = 2, with no remainder). That makes it a common multiple of 4 and 6. Why not the others? 8 comes from 4 but not 6; 14 isn’t divisible by either 4 or 6; 18 comes from 6 but isn’t divisible by 4. So 12 is the correct common multiple.

A number that is a multiple of both 4 and 6 is a common multiple of those two numbers. To find one, think of multiples of each: multiples of 4 are 4, 8, 12, 16, 20, … and multiples of 6 are 6, 12, 18, 24, …. The first number that appears in both lists is 12, so 12 is divisible by 4 and by 6 (12 ÷ 4 = 3 and 12 ÷ 6 = 2, with no remainder). That makes it a common multiple of 4 and 6.

Why not the others? 8 comes from 4 but not 6; 14 isn’t divisible by either 4 or 6; 18 comes from 6 but isn’t divisible by 4. So 12 is the correct common multiple.