Least Common Multiple of 105 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 105 and 113 the smallest integer that is 11865 that is divisible by both numbers.
Least Common Multiple (LCM) of 105 and 113 is 11865.
LCM(105,113) = 11865
LCM of 105 and 113
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 105 and 113 by Prime method
- Least Common Multiple of 105 and 113 with GCF Formula
LCM of 105 and 113 is 11865
Least common multiple can be found by multiplying the highest exponent prime factors of 105 and 113. First we will calculate the prime factors of 105 and 113.
Prime Factorization of 105
| 3 | 105 |
| 5 | 35 |
| 7 | 7 |
| 1 |
Prime factors of 105 are 3, 5,7. Prime factorization of 105 in exponential form is:
105 = 31×51×71
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 105 and 113.
LCM(105,113) = 31×51×71×1131
LCM(105,113) = 11865
Factors of 105
List of positive integer factors of 105 that divides 105 without a remainder.
1, 3, 5, 7, 15, 21, 35, 105
Factors of 113
List of positive integer factors of 113 that divides 113 without a remainder.
1, 113
Least Common Multiple of 105 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 105 and 113, than apply into the LCM equation.
GCF(105,113) = 1
LCM(105,113) = ( 105 × 113) / 1
LCM(105,113) = 11865 / 1
LCM(105,113) = 11865
Properties of LCM 105 and 113
(i) The LCM of 113 and 105 is associative
LCM of 105 and 113 = LCM of 113 and 105
Related Least Common Multiples of 105
Related Least Common Multiples of 113
Frequently Asked Questions on LCM of 105 and 113
1. What is the LCM of 105 and 113?
Answer: LCM of 105 and 113 is 11865.
2. What are the Factors of 105?
Answer: Factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. There are 8 integers that are factors of 105. The greatest factor of 105 is 105.
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 105 and 113?
Answer:
Least Common Multiple of 105 and 113 = 11865
Step 1: Find the prime factorization of 105
105 = 3 x 5 x 7
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 = 11865 = 3 x 5 x 7 x 113
Step 4: Therefore, the least common multiple of 105 and 113 is 11865.
