Least Common Multiple of 108 and 115
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 108 and 115 the smallest integer that is 12420 that is divisible by both numbers.
Least Common Multiple (LCM) of 108 and 115 is 12420.
LCM(108,115) = 12420
LCM of 108 and 115
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 108 and 115 by Prime method
- Least Common Multiple of 108 and 115 with GCF Formula
LCM of 108 and 115 is 12420
Least common multiple can be found by multiplying the highest exponent prime factors of 108 and 115. First we will calculate the prime factors of 108 and 115.
Prime Factorization of 108
| 2 | 108 |
| 2 | 54 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 108 are 2,3. Prime factorization of 108 in exponential form is:
108 = 22×33
Prime Factorization of 115
| 5 | 115 |
| 23 | 23 |
| 1 |
Prime factors of 115 are 5,23. Prime factorization of 115 in exponential form is:
115 = 51×231
Now multiplying the highest exponent prime factors to calculate the LCM of 108 and 115.
LCM(108,115) = 22×33×51×231
LCM(108,115) = 12420
Factors of 108
List of positive integer factors of 108 that divides 108 without a remainder.
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factors of 115
List of positive integer factors of 115 that divides 115 without a remainder.
1, 5, 23, 115
Least Common Multiple of 108 and 115 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 108 and 115, than apply into the LCM equation.
GCF(108,115) = 1
LCM(108,115) = ( 108 × 115) / 1
LCM(108,115) = 12420 / 1
LCM(108,115) = 12420
Properties of LCM 108 and 115
(i) The LCM of 115 and 108 is associative
LCM of 108 and 115 = LCM of 115 and 108
Related Least Common Multiples of 108
Related Least Common Multiples of 115
Frequently Asked Questions on LCM of 108 and 115
1. What is the LCM of 108 and 115?
Answer: LCM of 108 and 115 is 12420.
2. What are the Factors of 108?
Answer: Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. There are 12 integers that are factors of 108. The greatest factor of 108 is 108.
3. What are the Factors of 115?
Answer: Factors of 115 are 1, 5, 23, 115. There are 4 integers that are factors of 115. The greatest factor of 115 is 115.
4. How to Find the LCM of 108 and 115?
Answer:
Least Common Multiple of 108 and 115 = 12420
Step 1: Find the prime factorization of 108
108 = 2 x 2 x 3 x 3 x 3
Step 2: Find the prime factorization of 115
115 = 5 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 12420 = 2 x 2 x 3 x 3 x 3 x 5 x 23
Step 4: Therefore, the least common multiple of 108 and 115 is 12420.