Free LCM Calculator determines the least common multiple (LCM) between 8 and 12 the smallest integer that is 24 that is divisible by both numbers.
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Least Common Multiple (LCM) of 8 and 12 is 24.
LCM(8,12) = 24
Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 12. First we will calculate the prime factors of 8 and 12.
Prime Factorization of 8
| 2 | 8 |
| 2 | 4 |
| 2 | 2 |
| 1 |
Prime factors of 8 are 2. Prime factorization of 8 in exponential form is:
8 = 23Prime Factorization of 12
| 2 | 12 |
| 2 | 6 |
| 3 | 3 |
| 1 |
Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:
12 = 22×31Now multiplying the highest exponent prime factors to calculate the LCM of 8 and 12.
LCM(8,12) = 23×31LCM(8,12) = 24
Factors of 8
List of positive integer factors of 8 that divides 8 without a remainder.
1, 2, 4, 8
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1, 2, 3, 4, 6, 12
Least Common Multiple of 8 and 12 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).We need to calculate greatest common factor 8 and 12, than apply into the LCM equation.
GCF(8,12) = 4LCM(8,12) = ( 8 × 12) / 4LCM(8,12) = 96 / 4LCM(8,12) = 24
Properties of LCM 8 and 12
(i) The LCM of 12 and 8 is associative
LCM of 8 and 12 = LCM of 12 and 8
Related Least Common Multiples of 8
Related Least Common Multiples of 12
Frequently Asked Questions on LCM of 8 and 12
1. What is the LCM of 8 and 12?
Answer: LCM of 8 and 12 is 24.
2. What are the Factors of 8?
Answer: Factors of 8 are 1, 2, 4, 8. There are 4 integers that are factors of 8. The greatest factor of 8 is 8.
3. What are the Factors of 12?
Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.
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4. How to Find the LCM of 8 and 12?
Answer:
Least Common Multiple of 8 and 12 = 24
Step 1: Find the prime factorization of 8
8 = 2 x 2 x 2
Step 2: Find the prime factorization of 12
12 = 2 x 2 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 24 = 2 x 2 x 2 x 3
Step 4: Therefore, the least common multiple of 8 and 12 is 24.
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