Least Common Multiple of 106 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 106 and 111 the smallest integer that is 11766 that is divisible by both numbers.
Least Common Multiple (LCM) of 106 and 111 is 11766.
LCM(106,111) = 11766
LCM of 106 and 111
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 106 and 111 by Prime method
- Least Common Multiple of 106 and 111 with GCF Formula
LCM of 106 and 111 is 11766
Least common multiple can be found by multiplying the highest exponent prime factors of 106 and 111. First we will calculate the prime factors of 106 and 111.
Prime Factorization of 106
| 2 | 106 |
| 53 | 53 |
| 1 |
Prime factors of 106 are 2,53. Prime factorization of 106 in exponential form is:
106 = 21×531
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 106 and 111.
LCM(106,111) = 21×31×371×531
LCM(106,111) = 11766
Factors of 106
List of positive integer factors of 106 that divides 106 without a remainder.
1, 2, 53, 106
Factors of 111
List of positive integer factors of 111 that divides 111 without a remainder.
1, 3, 37, 111
Least Common Multiple of 106 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 106 and 111, than apply into the LCM equation.
GCF(106,111) = 1
LCM(106,111) = ( 106 × 111) / 1
LCM(106,111) = 11766 / 1
LCM(106,111) = 11766
Properties of LCM 106 and 111
(i) The LCM of 111 and 106 is associative
LCM of 106 and 111 = LCM of 111 and 106
Related Least Common Multiples of 106
Related Least Common Multiples of 111
Frequently Asked Questions on LCM of 106 and 111
1. What is the LCM of 106 and 111?
Answer: LCM of 106 and 111 is 11766.
2. What are the Factors of 106?
Answer: Factors of 106 are 1, 2, 53, 106. There are 4 integers that are factors of 106. The greatest factor of 106 is 106.
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 106 and 111?
Answer:
Least Common Multiple of 106 and 111 = 11766
Step 1: Find the prime factorization of 106
106 = 2 x 53
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 = 11766 = 2 x 3 x 37 x 53
Step 4: Therefore, the least common multiple of 106 and 111 is 11766.
