Least Common Multiple of 108 and 113
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 113 the smallest integer that is 12204 that is divisible by both numbers.
Least Common Multiple (LCM) of 108 and 113 is 12204.
LCM(108,113) = 12204
LCM of 108 and 113
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 108 and 113 by Prime method
- Least Common Multiple of 108 and 113 with GCF Formula
LCM of 108 and 113 is 12204
Least common multiple can be found by multiplying the highest exponent prime factors of 108 and 113. First we will calculate the prime factors of 108 and 113.
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 113
| 113 | 113 |
| 1 |
Prime factors of 113 are 113. Prime factorization of 113 in exponential form is:
113 = 1131
Now multiplying the highest exponent prime factors to calculate the LCM of 108 and 113.
LCM(108,113) = 22×33×1131
LCM(108,113) = 12204
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 113
List of positive integer factors of 113 that divides 113 without a remainder.
1, 113
Least Common Multiple of 108 and 113 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 113, than apply into the LCM equation.
GCF(108,113) = 1
LCM(108,113) = ( 108 × 113) / 1
LCM(108,113) = 12204 / 1
LCM(108,113) = 12204
Properties of LCM 108 and 113
(i) The LCM of 113 and 108 is associative
LCM of 108 and 113 = LCM of 113 and 108
Related Least Common Multiples of 108
Related Least Common Multiples of 113
Frequently Asked Questions on LCM of 108 and 113
1. What is the LCM of 108 and 113?
Answer: LCM of 108 and 113 is 12204.
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 113?
Answer: Factors of 113 are 1, 113. There are 2 integers that are factors of 113. The greatest factor of 113 is 113.
4. How to Find the LCM of 108 and 113?
Answer:
Least Common Multiple of 108 and 113 = 12204
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 113
113 = 113
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 12204 = 2 x 2 x 3 x 3 x 3 x 113
Step 4: Therefore, the least common multiple of 108 and 113 is 12204.