# lcm of 18 and 12

#### Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 18 and 12. To find the LCM, we will look for the smallest positive integer that is divisible by both numbers.

#### Answer

36
##### Answer for screen readers

The LCM of 18 and 12 is 36

#### Steps to Solve

1. Find the prime factors of each number

Prime factorization is breaking down each number into its prime factors.

• $18 = 2^1 imes 3^2$
• $12 = 2^2 imes 3^1$
1. Identify the highest powers of each prime number

To find the LCM, take the highest power of each prime number.

• The highest power of 2 is $2^2$ (from 12).
• The highest power of 3 is $3^2$ (from 18).
1. Multiply these highest powers together

Multiply these values to find the LCM:

$$LCM = 2^2 \times 3^2$$ $$LCM = 4 \times 9$$

$$LCM = 36$$

The LCM of 18 and 12 is 36

#### More Information

The least common multiple (LCM) of two integers is the smallest positive integer that is divisible by both numbers. It's useful for finding common denominators in fractions.

#### Tips

A common mistake is not using the highest powers of each prime factor when finding the LCM.

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