Least Common Multiple of 108 and 111
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 111 the smallest integer that is 3996 that is divisible by both numbers.
Least Common Multiple (LCM) of 108 and 111 is 3996.
LCM(108,111) = 3996
LCM of 108 and 111
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 108 and 111 by Prime method
- Least Common Multiple of 108 and 111 with GCF Formula
LCM of 108 and 111 is 3996
Least common multiple can be found by multiplying the highest exponent prime factors of 108 and 111. First we will calculate the prime factors of 108 and 111.
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 111
| 3 | 111 |
| 37 | 37 |
| 1 |
Prime factors of 111 are 3,37. Prime factorization of 111 in exponential form is:
111 = 31×371
Now multiplying the highest exponent prime factors to calculate the LCM of 108 and 111.
LCM(108,111) = 22×33×371
LCM(108,111) = 3996
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 111
List of positive integer factors of 111 that divides 111 without a remainder.
1, 3, 37, 111
Least Common Multiple of 108 and 111 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 111, than apply into the LCM equation.
GCF(108,111) = 3
LCM(108,111) = ( 108 × 111) / 3
LCM(108,111) = 11988 / 3
LCM(108,111) = 3996
Properties of LCM 108 and 111
(i) The LCM of 111 and 108 is associative
LCM of 108 and 111 = LCM of 111 and 108
Related Least Common Multiples of 108
Related Least Common Multiples of 111
Frequently Asked Questions on LCM of 108 and 111
1. What is the LCM of 108 and 111?
Answer: LCM of 108 and 111 is 3996.
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 111?
Answer: Factors of 111 are 1, 3, 37, 111. There are 4 integers that are factors of 111. The greatest factor of 111 is 111.
4. How to Find the LCM of 108 and 111?
Answer:
Least Common Multiple of 108 and 111 = 3996
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 111
111 = 3 x 37
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3996 = 2 x 2 x 3 x 3 x 3 x 37
Step 4: Therefore, the least common multiple of 108 and 111 is 3996.