Least Common Multiple of 100 and 107
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 100 and 107 the smallest integer that is 10700 that is divisible by both numbers.
Least Common Multiple (LCM) of 100 and 107 is 10700.
LCM(100,107) = 10700
LCM of 100 and 107
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 100 and 107 by Prime method
- Least Common Multiple of 100 and 107 with GCF Formula
LCM of 100 and 107 is 10700
Least common multiple can be found by multiplying the highest exponent prime factors of 100 and 107. First we will calculate the prime factors of 100 and 107.
Prime Factorization of 100
| 2 | 100 |
| 2 | 50 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 100 are 2,5. Prime factorization of 100 in exponential form is:
100 = 22×52
Prime Factorization of 107
| 107 | 107 |
| 1 |
Prime factors of 107 are 107. Prime factorization of 107 in exponential form is:
107 = 1071
Now multiplying the highest exponent prime factors to calculate the LCM of 100 and 107.
LCM(100,107) = 22×52×1071
LCM(100,107) = 10700
Factors of 100
List of positive integer factors of 100 that divides 100 without a remainder.
1, 2, 4, 5, 10, 20, 25, 50, 100
Factors of 107
List of positive integer factors of 107 that divides 107 without a remainder.
1, 107
Least Common Multiple of 100 and 107 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 100 and 107, than apply into the LCM equation.
GCF(100,107) = 1
LCM(100,107) = ( 100 × 107) / 1
LCM(100,107) = 10700 / 1
LCM(100,107) = 10700
Properties of LCM 100 and 107
(i) The LCM of 107 and 100 is associative
LCM of 100 and 107 = LCM of 107 and 100
Related Least Common Multiples of 100
Related Least Common Multiples of 107
Frequently Asked Questions on LCM of 100 and 107
1. What is the LCM of 100 and 107?
Answer: LCM of 100 and 107 is 10700.
2. What are the Factors of 100?
Answer: Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. There are 9 integers that are factors of 100. The greatest factor of 100 is 100.
3. What are the Factors of 107?
Answer: Factors of 107 are 1, 107. There are 2 integers that are factors of 107. The greatest factor of 107 is 107.
4. How to Find the LCM of 100 and 107?
Answer:
Least Common Multiple of 100 and 107 = 10700
Step 1: Find the prime factorization of 100
100 = 2 x 2 x 5 x 5
Step 2: Find the prime factorization of 107
107 = 107
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 10700 = 2 x 2 x 5 x 5 x 107
Step 4: Therefore, the least common multiple of 100 and 107 is 10700.