Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 113 and 114 the smallest integer that is 12882 that is divisible by both numbers.
Least Common Multiple (LCM) of 113 and 114 is 12882.
LCM(113,114) = 12882
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 113 and 114. First we will calculate the prime factors of 113 and 114.
Prime Factorization of 113
113 | 113 |
1 |
Prime factors of 113 are 113. Prime factorization of 113 in exponential form is:
113 = 1131
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 113 and 114.
LCM(113,114) = 21×31×191×1131
LCM(113,114) = 12882
Factors of 113
List of positive integer factors of 113 that divides 113 without a remainder.
1, 113
Factors of 114
List of positive integer factors of 114 that divides 114 without a remainder.
1, 2, 3, 6, 19, 38, 57, 114
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 113 and 114, than apply into the LCM equation.
GCF(113,114) = 1
LCM(113,114) = ( 113 × 114) / 1
LCM(113,114) = 12882 / 1
LCM(113,114) = 12882
(i) The LCM of 114 and 113 is associative
LCM of 113 and 114 = LCM of 114 and 113
1. What is the LCM of 113 and 114?
Answer: LCM of 113 and 114 is 12882.
2. 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.
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 113 and 114?
Answer:
Least Common Multiple of 113 and 114 = 12882
Step 1: Find the prime factorization of 113
113 = 113
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 = 12882 = 2 x 3 x 19 x 113
Step 4: Therefore, the least common multiple of 113 and 114 is 12882.