Least Common Multiple of 106 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 106 and 113 the smallest integer that is 11978 that is divisible by both numbers.
Least Common Multiple (LCM) of 106 and 113 is 11978.
LCM(106,113) = 11978
LCM of 106 and 113
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 106 and 113 by Prime method
- Least Common Multiple of 106 and 113 with GCF Formula
LCM of 106 and 113 is 11978
Least common multiple can be found by multiplying the highest exponent prime factors of 106 and 113. First we will calculate the prime factors of 106 and 113.
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 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 106 and 113.
LCM(106,113) = 21×531×1131
LCM(106,113) = 11978
Factors of 106
List of positive integer factors of 106 that divides 106 without a remainder.
1, 2, 53, 106
Factors of 113
List of positive integer factors of 113 that divides 113 without a remainder.
1, 113
Least Common Multiple of 106 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 106 and 113, than apply into the LCM equation.
GCF(106,113) = 1
LCM(106,113) = ( 106 × 113) / 1
LCM(106,113) = 11978 / 1
LCM(106,113) = 11978
Properties of LCM 106 and 113
(i) The LCM of 113 and 106 is associative
LCM of 106 and 113 = LCM of 113 and 106
Related Least Common Multiples of 106
Related Least Common Multiples of 113
Frequently Asked Questions on LCM of 106 and 113
1. What is the LCM of 106 and 113?
Answer: LCM of 106 and 113 is 11978.
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 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 106 and 113?
Answer:
Least Common Multiple of 106 and 113 = 11978
Step 1: Find the prime factorization of 106
106 = 2 x 53
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 = 11978 = 2 x 53 x 113
Step 4: Therefore, the least common multiple of 106 and 113 is 11978.
