What is the least common multiple (LCM) of 9 and 12?
36
18
72
24
of 10
LCM of 9 and 12 – How to find in Different Ways
LCM of 9 and 12 – How to find in Different Ways
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.
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Practice Test
Which of the following is not a multiple of the LCM of 9 and 12?
72
54
48
108
of 10
If you have a number that is a multiple of both 9 and 12, which of the following numbers could it be?
108
45
63
27
of 10
What is the smallest number that both 9 and 12 divide evenly into?
72
36
24
18
of 10
Which of the following pairs of numbers have an LCM of 36?
9 and 12
6 and 18
4 and 9
8 and 12
of 10
How many times does the LCM of 9 and 12 fit into 108?
2
3
4
6
of 10
If you multiply the LCM of 9 and 12 by 2, what is the resulting number?
72
54
48
36
of 10
What is the LCM of 9, 12, and another number that makes it 108?
27
24
18
36
of 10
Which of the following is a common multiple of 9 and 12, but not the LCM?
72
108
45
54
of 10
What is the LCM of 9, 12, and 27?
36
72
108
54
of 10