Which of the following is the least common multiple of 4 and 6?

Which of the following is the least common multiple of 4 and 6?

• A. 12
• B. 18
• C. 24
• D. 30

Answer: (A)

To determine the least common multiple (LCM) of two numbers, we seek the smallest positive integer that is a multiple of both numbers. For the numbers 4 and 6, the multiples of 4 are 4, 8, 12, 16, 20, 24, and so on. For the number 6, the multiples are 6, 12, 18, 24, 30, and so on. From these lists, the smallest common multiple that appears in both is 12. 12 is the first number to show up in both lists, making it the least common multiple. In this case, since it is the smallest number that both 4 and 6 can divide without leaving a remainder, it qualifies as the LCM of the two numbers. Understanding the concept of multiples helps solidify why 12 is the correct answer, as it confirms that it is both a product of the two numbers and the least of such products.

To determine the least common multiple (LCM) of two numbers, we seek the smallest positive integer that is a multiple of both numbers.

For the numbers 4 and 6, the multiples of 4 are 4, 8, 12, 16, 20, 24, and so on. For the number 6, the multiples are 6, 12, 18, 24, 30, and so on. From these lists, the smallest common multiple that appears in both is 12.

12 is the first number to show up in both lists, making it the least common multiple. In this case, since it is the smallest number that both 4 and 6 can divide without leaving a remainder, it qualifies as the LCM of the two numbers.

Understanding the concept of multiples helps solidify why 12 is the correct answer, as it confirms that it is both a product of the two numbers and the least of such products.