Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8 and 27 the smallest integer that is 216 that is divisible by both numbers.
Least Common Multiple (LCM) of 8 and 27 is 216.
LCM(8,27) = 216
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 8 and 27. First we will calculate the prime factors of 8 and 27.
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 = 23
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 8 and 27.
LCM(8,27) = 23×33
LCM(8,27) = 216
Factors of 8
List of positive integer factors of 8 that divides 8 without a remainder.
1, 2, 4, 8
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 8 and 27, than apply into the LCM equation.
GCF(8,27) = 1
LCM(8,27) = ( 8 × 27) / 1
LCM(8,27) = 216 / 1
LCM(8,27) = 216
(i) The LCM of 27 and 8 is associative
LCM of 8 and 27 = LCM of 27 and 8
1. What is the LCM of 8 and 27?
Answer: LCM of 8 and 27 is 216.
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 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 8 and 27?
Answer:
Least Common Multiple of 8 and 27 = 216
Step 1: Find the prime factorization of 8
8 = 2 x 2 x 2
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 = 216 = 2 x 2 x 2 x 3 x 3 x 3
Step 4: Therefore, the least common multiple of 8 and 27 is 216.