Question

The number 108 is the LCM of 36 and 54. List the next common multiple of 36 and 54. Explain your reasoning.

Answer 1

To find the next common multiple of 36 and 54 after 108, we can start by using the concept of multiples. The least common multiple (LCM) of two numbers is the smallest positive integer that is a multiple of both numbers. Since 108 is the LCM of 36 and 54, the next common multiple will be the next integer that is a multiple of both numbers.

To find these multiples, we can calculate the multiples of the LCM (108):

1. The first common multiple is \( 108 \times 1 = 108 \).
2. The next common multiple is \( 108 \times 2 = 216 \).

Thus, the next common multiple of 36 and 54 after 108 is **216**.

To ensure clarity, we can also verify that 216 is indeed a multiple of both 36 and 54:

- **For 36**:
\[
216 \div 36 = 6
\]
(which is an integer, confirming that 216 is a multiple of 36).

- **For 54**:
\[
216 \div 54 = 4
\]
(which is also an integer, confirming that 216 is a multiple of 54).

Thus, the next common multiple of 36 and 54 is indeed **216**.