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?

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 Listing Multiples

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.