Least Common Multiple of 546 and 549
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 546 and 549 the smallest integer that is 99918 that is divisible by both numbers.
Least Common Multiple (LCM) of 546 and 549 is 99918.
LCM(546,549) = 99918
LCM of 546 and 549
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 546 and 549 by Prime method
- Least Common Multiple of 546 and 549 with GCF Formula
LCM of 546 and 549 is 99918
Least common multiple can be found by multiplying the highest exponent prime factors of 546 and 549. First we will calculate the prime factors of 546 and 549.
Prime Factorization of 546
| 2 | 546 |
| 3 | 273 |
| 7 | 91 |
| 13 | 13 |
| 1 |
Prime factors of 546 are 2, 3, 7,13. Prime factorization of 546 in exponential form is:
546 = 21×31×71×131
Prime Factorization of 549
| 3 | 549 |
| 3 | 183 |
| 61 | 61 |
| 1 |
Prime factors of 549 are 3,61. Prime factorization of 549 in exponential form is:
549 = 32×611
Now multiplying the highest exponent prime factors to calculate the LCM of 546 and 549.
LCM(546,549) = 21×32×71×131×611
LCM(546,549) = 99918
Factors of 546
List of positive integer factors of 546 that divides 546 without a remainder.
1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
Factors of 549
List of positive integer factors of 549 that divides 549 without a remainder.
1, 3, 9, 61, 183, 549
Least Common Multiple of 546 and 549 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 546 and 549, than apply into the LCM equation.
GCF(546,549) = 3
LCM(546,549) = ( 546 × 549) / 3
LCM(546,549) = 299754 / 3
LCM(546,549) = 99918
Properties of LCM 546 and 549
(i) The LCM of 549 and 546 is associative
LCM of 546 and 549 = LCM of 549 and 546
Related Least Common Multiples of 546
Related Least Common Multiples of 549
Frequently Asked Questions on LCM of 546 and 549
1. What is the LCM of 546 and 549?
Answer: LCM of 546 and 549 is 99918.
2. What are the Factors of 546?
Answer: Factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546. There are 16 integers that are factors of 546. The greatest factor of 546 is 546.
3. What are the Factors of 549?
Answer: Factors of 549 are 1, 3, 9, 61, 183, 549. There are 6 integers that are factors of 549. The greatest factor of 549 is 549.
4. How to Find the LCM of 546 and 549?
Answer:
Least Common Multiple of 546 and 549 = 99918
Step 1: Find the prime factorization of 546
546 = 2 x 3 x 7 x 13
Step 2: Find the prime factorization of 549
549 = 3 x 3 x 61
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 99918 = 2 x 3 x 3 x 7 x 13 x 61
Step 4: Therefore, the least common multiple of 546 and 549 is 99918.