## LCM of 9 and 12

The LCM of 9 and 12 is the smallest number that is a multiple of both 9 and 12. The initial multiples of 9 are 9, 18, 27, 36, 45, etc., and those of 12 are 12, 24, 36, 48, 60, etc. To find the LCM of 9 and 12, you can use the division method, list multiples, or perform prime factorization.

## What is the LCM of 9 and 12?

**LCM of 9 and 12 is 36.**

The Least Common Multiple (LCM) of 9 and 12 is 36, which is the smallest number that both 9 and 12 can evenly divide. This ensures 36 is a common multiple of both numbers.

## Methods to Find LCM of 9 and 12

- Division Method
- Listing Multiples
- Prime Factorization Method

## LCM of 9 and 12 by Division Method]

**Write the numbers side by side:**- Place 9 and 12 next to each other.

**Divide by the smallest prime number:**- Divide both numbers by 2 (the smallest prime number that can divide 12).
- Write the quotient below each number: 9 remains 9, and 12 becomes 6.
- 12/2=6

**Repeat the division:**- Divide by 2 again: 9 remains 9, and 6 becomes 3.
- 6/2=3

**Divide by the next smallest prime number:**- Divide by 3: 9 becomes 3, and 3 becomes 1.
- 9/3=3
- 3/3=1

**Continue until both numbers become 1:**- Divide 3 by 3: 3 becomes 1, and 1 remains 1.
- 3/3=1

**Multiply all the divisors:**- Multiply all the prime divisors used: 2×2×3=12
- This is an error in the image. Correct the multiplication to:
- 2×2×3×3=362×2×3×3=36

**Result:**- The LCM of 9 and 12 is 36.

## LCM of 9 and 12 by Listing Multiples

## LCM of 9 and 12 by Prime Factorization

**Prime Factorization:****9**: 9=3²**12**: 12=2²×3

**Identify the Highest Powers of All Prime Factors:**- For 2: The highest power is 2².
- For 3: The highest power is 3².

**Multiply the Highest Powers of All Prime Factors:**- 2²×3²= 4×9 = 36

### Result:

- The LCM of 9 and 12 is
**36**.

**How is the LCM of 9 and 12 found?**

The LCM can be found using prime factorization, listing multiples, or the division method.

**Why is the LCM of 9 and 12 important?**

The LCM is useful for solving problems involving common multiples, such as adding or subtracting fractions with different denominators.

**Can the LCM of 9 and 12 be smaller than 36?**

No, 36 is the smallest number that both 9 and 12 can divide without leaving a remainder.

**Is 36 a common multiple of both 9 and 12?**

Yes, 36 is a common multiple and is the smallest number that both 9 and 12 can divide evenly.

**What are the multiples of 9 and 12?**

Multiples of 9 are 9, 18, 27, 36, etc., and multiples of 12 are 12, 24, 36, 48, etc.