Least Common Multiple of 96 and 99
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 96 and 99 the smallest integer that is 3168 that is divisible by both numbers.
Least Common Multiple (LCM) of 96 and 99 is 3168.
LCM(96,99) = 3168
LCM of 96 and 99
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 96 and 99 by Prime method
- Least Common Multiple of 96 and 99 with GCF Formula
LCM of 96 and 99 is 3168
Least common multiple can be found by multiplying the highest exponent prime factors of 96 and 99. First we will calculate the prime factors of 96 and 99.
Prime Factorization of 96
| 2 | 96 |
| 2 | 48 |
| 2 | 24 |
| 2 | 12 |
| 2 | 6 |
| 3 | 3 |
| 1 |
Prime factors of 96 are 2,3. Prime factorization of 96 in exponential form is:
96 = 25×31
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
Now multiplying the highest exponent prime factors to calculate the LCM of 96 and 99.
LCM(96,99) = 25×32×111
LCM(96,99) = 3168
Factors of 96
List of positive integer factors of 96 that divides 96 without a remainder.
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 99
List of positive integer factors of 99 that divides 99 without a remainder.
1, 3, 9, 11, 33, 99
Least Common Multiple of 96 and 99 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 96 and 99, than apply into the LCM equation.
GCF(96,99) = 3
LCM(96,99) = ( 96 × 99) / 3
LCM(96,99) = 9504 / 3
LCM(96,99) = 3168
Properties of LCM 96 and 99
(i) The LCM of 99 and 96 is associative
LCM of 96 and 99 = LCM of 99 and 96
Related Least Common Multiples of 96
Related Least Common Multiples of 99
Frequently Asked Questions on LCM of 96 and 99
1. What is the LCM of 96 and 99?
Answer: LCM of 96 and 99 is 3168.
2. What are the Factors of 96?
Answer: Factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96. There are 12 integers that are factors of 96. The greatest factor of 96 is 96.
3. 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.
4. How to Find the LCM of 96 and 99?
Answer:
Least Common Multiple of 96 and 99 = 3168
Step 1: Find the prime factorization of 96
96 = 2 x 2 x 2 x 2 x 2 x 3
Step 2: Find the prime factorization of 99
99 = 3 x 3 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3168 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 11
Step 4: Therefore, the least common multiple of 96 and 99 is 3168.
