Least Common Multiple of 106 and 114
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 114 the smallest integer that is 6042 that is divisible by both numbers.
Least Common Multiple (LCM) of 106 and 114 is 6042.
LCM(106,114) = 6042
LCM of 106 and 114
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 106 and 114 by Prime method
- Least Common Multiple of 106 and 114 with GCF Formula
LCM of 106 and 114 is 6042
Least common multiple can be found by multiplying the highest exponent prime factors of 106 and 114. First we will calculate the prime factors of 106 and 114.
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 114
| 2 | 114 |
| 3 | 57 |
| 19 | 19 |
| 1 |
Prime factors of 114 are 2, 3,19. Prime factorization of 114 in exponential form is:
114 = 21×31×191
Now multiplying the highest exponent prime factors to calculate the LCM of 106 and 114.
LCM(106,114) = 21×31×191×531
LCM(106,114) = 6042
Factors of 106
List of positive integer factors of 106 that divides 106 without a remainder.
1, 2, 53, 106
Factors of 114
List of positive integer factors of 114 that divides 114 without a remainder.
1, 2, 3, 6, 19, 38, 57, 114
Least Common Multiple of 106 and 114 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 114, than apply into the LCM equation.
GCF(106,114) = 2
LCM(106,114) = ( 106 × 114) / 2
LCM(106,114) = 12084 / 2
LCM(106,114) = 6042
Properties of LCM 106 and 114
(i) The LCM of 114 and 106 is associative
LCM of 106 and 114 = LCM of 114 and 106
Related Least Common Multiples of 106
Related Least Common Multiples of 114
Frequently Asked Questions on LCM of 106 and 114
1. What is the LCM of 106 and 114?
Answer: LCM of 106 and 114 is 6042.
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 114?
Answer: Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. There are 8 integers that are factors of 114. The greatest factor of 114 is 114.
4. How to Find the LCM of 106 and 114?
Answer:
Least Common Multiple of 106 and 114 = 6042
Step 1: Find the prime factorization of 106
106 = 2 x 53
Step 2: Find the prime factorization of 114
114 = 2 x 3 x 19
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 6042 = 2 x 3 x 19 x 53
Step 4: Therefore, the least common multiple of 106 and 114 is 6042.