What is the lcm of 9 and 15

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what is the lcm of 9 and 15

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What is the LCM of 9 and 15?

Answer: To find the Least Common Multiple (LCM) of 9 and 15, follow these steps:

1. Prime Factorizations:

First, find the prime factorizations of the numbers 9 and 15.

  • Prime factorization of 9:
9 = 3^2
  • Prime factorization of 15:
15 = 3 \times 5

2. Determine the LCM:

To determine the LCM, take the highest power of each prime number that appears in the factorizations.

  • For the prime number 3, the highest power is (3^2).
  • For the prime number 5, the highest power is (5^1).

Thus, the LCM is:

\text{LCM} = 3^2 \times 5^1

3. Calculate the LCM:

Now, calculate the LCM by multiplying these values:

3^2 = 9
9 \times 5 = 45

Therefore, the LCM of 9 and 15 is (\boxed{45}).

This means the smallest number that both 9 and 15 can divide into without leaving a remainder is 45.

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