Least Common Multiple of 100 and 105
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 105 the smallest integer that is 2100 that is divisible by both numbers.
Least Common Multiple (LCM) of 100 and 105 is 2100.
LCM(100,105) = 2100
LCM of 100 and 105
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 100 and 105 by Prime method
- Least Common Multiple of 100 and 105 with GCF Formula
LCM of 100 and 105 is 2100
Least common multiple can be found by multiplying the highest exponent prime factors of 100 and 105. First we will calculate the prime factors of 100 and 105.
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 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
Now multiplying the highest exponent prime factors to calculate the LCM of 100 and 105.
LCM(100,105) = 22×31×52×71
LCM(100,105) = 2100
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 105
List of positive integer factors of 105 that divides 105 without a remainder.
1, 3, 5, 7, 15, 21, 35, 105
Least Common Multiple of 100 and 105 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 105, than apply into the LCM equation.
GCF(100,105) = 5
LCM(100,105) = ( 100 × 105) / 5
LCM(100,105) = 10500 / 5
LCM(100,105) = 2100
Properties of LCM 100 and 105
(i) The LCM of 105 and 100 is associative
LCM of 100 and 105 = LCM of 105 and 100
Related Least Common Multiples of 100
Related Least Common Multiples of 105
Frequently Asked Questions on LCM of 100 and 105
1. What is the LCM of 100 and 105?
Answer: LCM of 100 and 105 is 2100.
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 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.
4. How to Find the LCM of 100 and 105?
Answer:
Least Common Multiple of 100 and 105 = 2100
Step 1: Find the prime factorization of 100
100 = 2 x 2 x 5 x 5
Step 2: Find the prime factorization of 105
105 = 3 x 5 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2100 = 2 x 2 x 3 x 5 x 5 x 7
Step 4: Therefore, the least common multiple of 100 and 105 is 2100.