Least Common Multiple of 99 and 104
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 104 the smallest integer that is 10296 that is divisible by both numbers.
Least Common Multiple (LCM) of 99 and 104 is 10296.
LCM(99,104) = 10296
LCM of 99 and 104
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 99 and 104 by Prime method
- Least Common Multiple of 99 and 104 with GCF Formula
LCM of 99 and 104 is 10296
Least common multiple can be found by multiplying the highest exponent prime factors of 99 and 104. First we will calculate the prime factors of 99 and 104.
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 104
| 2 | 104 |
| 2 | 52 |
| 2 | 26 |
| 13 | 13 |
| 1 |
Prime factors of 104 are 2,13. Prime factorization of 104 in exponential form is:
104 = 23×131
Now multiplying the highest exponent prime factors to calculate the LCM of 99 and 104.
LCM(99,104) = 23×32×111×131
LCM(99,104) = 10296
Factors of 99
List of positive integer factors of 99 that divides 99 without a remainder.
1, 3, 9, 11, 33, 99
Factors of 104
List of positive integer factors of 104 that divides 104 without a remainder.
1, 2, 4, 8, 13, 26, 52, 104
Least Common Multiple of 99 and 104 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 104, than apply into the LCM equation.
GCF(99,104) = 1
LCM(99,104) = ( 99 × 104) / 1
LCM(99,104) = 10296 / 1
LCM(99,104) = 10296
Properties of LCM 99 and 104
(i) The LCM of 104 and 99 is associative
LCM of 99 and 104 = LCM of 104 and 99
Related Least Common Multiples of 99
Related Least Common Multiples of 104
Frequently Asked Questions on LCM of 99 and 104
1. What is the LCM of 99 and 104?
Answer: LCM of 99 and 104 is 10296.
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 104?
Answer: Factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104. There are 8 integers that are factors of 104. The greatest factor of 104 is 104.
4. How to Find the LCM of 99 and 104?
Answer:
Least Common Multiple of 99 and 104 = 10296
Step 1: Find the prime factorization of 99
99 = 3 x 3 x 11
Step 2: Find the prime factorization of 104
104 = 2 x 2 x 2 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 10296 = 2 x 2 x 2 x 3 x 3 x 11 x 13
Step 4: Therefore, the least common multiple of 99 and 104 is 10296.
