Least Common Multiple of 99 and 100
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 99 and 100 the smallest integer that is 9900 that is divisible by both numbers.
Least Common Multiple (LCM) of 99 and 100 is 9900.
LCM(99,100) = 9900
LCM of 99 and 100
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 99 and 100 by Prime method
- Least Common Multiple of 99 and 100 with GCF Formula
LCM of 99 and 100 is 9900
Least common multiple can be found by multiplying the highest exponent prime factors of 99 and 100. First we will calculate the prime factors of 99 and 100.
Prime Factorization of 99
| 3 | 99 |
| 3 | 33 |
| 11 | 11 |
| 1 |
Prime factors of 99 are 3,11. Prime factorization of 99 in exponential form is:
99 = 32×111
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
Now multiplying the highest exponent prime factors to calculate the LCM of 99 and 100.
LCM(99,100) = 22×32×52×111
LCM(99,100) = 9900
Factors of 99
List of positive integer factors of 99 that divides 99 without a remainder.
1, 3, 9, 11, 33, 99
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
Least Common Multiple of 99 and 100 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 99 and 100, than apply into the LCM equation.
GCF(99,100) = 1
LCM(99,100) = ( 99 × 100) / 1
LCM(99,100) = 9900 / 1
LCM(99,100) = 9900
Properties of LCM 99 and 100
(i) The LCM of 100 and 99 is associative
LCM of 99 and 100 = LCM of 100 and 99
Related Least Common Multiples of 99
Related Least Common Multiples of 100
Frequently Asked Questions on LCM of 99 and 100
1. What is the LCM of 99 and 100?
Answer: LCM of 99 and 100 is 9900.
2. What are the Factors of 99?
Answer: Factors of 99 are 1, 3, 9, 11, 33, 99. There are 6 integers that are factors of 99. The greatest factor of 99 is 99.
3. 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.
4. How to Find the LCM of 99 and 100?
Answer:
Least Common Multiple of 99 and 100 = 9900
Step 1: Find the prime factorization of 99
99 = 3 x 3 x 11
Step 2: Find the prime factorization of 100
100 = 2 x 2 x 5 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 9900 = 2 x 2 x 3 x 3 x 5 x 5 x 11
Step 4: Therefore, the least common multiple of 99 and 100 is 9900.