Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 12 and 27 the smallest integer that is 108 that is divisible by both numbers.
Least Common Multiple (LCM) of 12 and 27 is 108.
LCM(12,27) = 108
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 12 and 27. First we will calculate the prime factors of 12 and 27.
Prime 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 = 22×31
Prime Factorization of 27
3 | 27 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:
27 = 33
Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 27.
LCM(12,27) = 22×33
LCM(12,27) = 108
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1, 2, 3, 4, 6, 12
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1, 3, 9, 27
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12 and 27, than apply into the LCM equation.
GCF(12,27) = 3
LCM(12,27) = ( 12 × 27) / 3
LCM(12,27) = 324 / 3
LCM(12,27) = 108
(i) The LCM of 27 and 12 is associative
LCM of 12 and 27 = LCM of 27 and 12
1. What is the LCM of 12 and 27?
Answer: LCM of 12 and 27 is 108.
2. 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.
3. What are the Factors of 27?
Answer: Factors of 27 are 1, 3, 9, 27. There are 4 integers that are factors of 27. The greatest factor of 27 is 27.
4. How to Find the LCM of 12 and 27?
Answer:
Least Common Multiple of 12 and 27 = 108
Step 1: Find the prime factorization of 12
12 = 2 x 2 x 3
Step 2: Find the prime factorization of 27
27 = 3 x 3 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 = 108 = 2 x 2 x 3 x 3 x 3
Step 4: Therefore, the least common multiple of 12 and 27 is 108.