# LCM of 9 and 12

Created by: Team Maths - Examples.com, Last Updated: August 23, 2024

## 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

1. Division Method
2. Listing Multiples
3. Prime Factorization Method

## LCM of 9 and 12 by Division Method]

1. Write the numbers side by side:
• Place 9 and 12 next to each other.
2. 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
3. Repeat the division:
• Divide by 2 again: 9 remains 9, and 6 becomes 3.
• 6/2=3
4. Divide by the next smallest prime number:
• Divide by 3: 9 becomes 3, and 3 becomes 1.
• 9/3=3
• 3/3=1
5. Continue until both numbers become 1:
• Divide 3 by 3: 3 becomes 1, and 1 remains 1.
• 3/3=1
6. 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
7. Result:
• The LCM of 9 and 12 is 36.

## LCM of 9 and 12 by Prime Factorization

1. Prime Factorization:
• 9: 9=3²
• 12: 12=2²×3
2. Identify the Highest Powers of All Prime Factors:
• For 2: The highest power is 2².
• For 3: The highest power is 3².
3. 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.

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