Least Common Multiple of 84 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 84 and 99 the smallest integer that is 2772 that is divisible by both numbers.
Least Common Multiple (LCM) of 84 and 99 is 2772.
LCM(84,99) = 2772
LCM of 84 and 99
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 84 and 99 by Prime method
- Least Common Multiple of 84 and 99 with GCF Formula
LCM of 84 and 99 is 2772
Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 99. First we will calculate the prime factors of 84 and 99.
Prime Factorization of 84
| 2 | 84 |
| 2 | 42 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 84 are 2, 3,7. Prime factorization of 84 in exponential form is:
84 = 22×31×71
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 84 and 99.
LCM(84,99) = 22×32×71×111
LCM(84,99) = 2772
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
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 84 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 84 and 99, than apply into the LCM equation.
GCF(84,99) = 3
LCM(84,99) = ( 84 × 99) / 3
LCM(84,99) = 8316 / 3
LCM(84,99) = 2772
Properties of LCM 84 and 99
(i) The LCM of 99 and 84 is associative
LCM of 84 and 99 = LCM of 99 and 84
Related Least Common Multiples of 84
Related Least Common Multiples of 99
Frequently Asked Questions on LCM of 84 and 99
1. What is the LCM of 84 and 99?
Answer: LCM of 84 and 99 is 2772.
2. What are the Factors of 84?
Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.
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 84 and 99?
Answer:
Least Common Multiple of 84 and 99 = 2772
Step 1: Find the prime factorization of 84
84 = 2 x 2 x 3 x 7
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 = 2772 = 2 x 2 x 3 x 3 x 7 x 11
Step 4: Therefore, the least common multiple of 84 and 99 is 2772.
