Least Common Multiple of 99 and 102
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 102 the smallest integer that is 3366 that is divisible by both numbers.
Least Common Multiple (LCM) of 99 and 102 is 3366.
LCM(99,102) = 3366
LCM of 99 and 102
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 99 and 102 by Prime method
- Least Common Multiple of 99 and 102 with GCF Formula
LCM of 99 and 102 is 3366
Least common multiple can be found by multiplying the highest exponent prime factors of 99 and 102. First we will calculate the prime factors of 99 and 102.
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 102
| 2 | 102 |
| 3 | 51 |
| 17 | 17 |
| 1 |
Prime factors of 102 are 2, 3,17. Prime factorization of 102 in exponential form is:
102 = 21×31×171
Now multiplying the highest exponent prime factors to calculate the LCM of 99 and 102.
LCM(99,102) = 21×32×111×171
LCM(99,102) = 3366
Factors of 99
List of positive integer factors of 99 that divides 99 without a remainder.
1, 3, 9, 11, 33, 99
Factors of 102
List of positive integer factors of 102 that divides 102 without a remainder.
1, 2, 3, 6, 17, 34, 51, 102
Least Common Multiple of 99 and 102 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 102, than apply into the LCM equation.
GCF(99,102) = 3
LCM(99,102) = ( 99 × 102) / 3
LCM(99,102) = 10098 / 3
LCM(99,102) = 3366
Properties of LCM 99 and 102
(i) The LCM of 102 and 99 is associative
LCM of 99 and 102 = LCM of 102 and 99
Related Least Common Multiples of 99
Related Least Common Multiples of 102
Frequently Asked Questions on LCM of 99 and 102
1. What is the LCM of 99 and 102?
Answer: LCM of 99 and 102 is 3366.
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 102?
Answer: Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. There are 8 integers that are factors of 102. The greatest factor of 102 is 102.
4. How to Find the LCM of 99 and 102?
Answer:
Least Common Multiple of 99 and 102 = 3366
Step 1: Find the prime factorization of 99
99 = 3 x 3 x 11
Step 2: Find the prime factorization of 102
102 = 2 x 3 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3366 = 2 x 3 x 3 x 11 x 17
Step 4: Therefore, the least common multiple of 99 and 102 is 3366.