Least Common Multiple of 540 and 546

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 540 and 546 the smallest integer that is 49140 that is divisible by both numbers.

Least Common Multiple (LCM) of 540 and 546 is 49140.

LCM(540,546) = 49140

LCM of 540 and 546

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 540 and 546

LCM of 540 and 546 is 49140

Least common multiple can be found by multiplying the highest exponent prime factors of 540 and 546. First we will calculate the prime factors of 540 and 546.

Prime Factorization of 540


2 540
2 270
3 135
3 45
3 15
5 5
1

Prime factors of 540 are 2, 3,5. Prime factorization of 540 in exponential form is:

540 = 22×33×51

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

Now multiplying the highest exponent prime factors to calculate the LCM of 540 and 546.

LCM(540,546) = 22×33×51×71×131
LCM(540,546) = 49140

Factors of 540

List of positive integer factors of 540 that divides 540 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540

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

Least Common Multiple of 540 and 546 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 540 and 546, than apply into the LCM equation.

GCF(540,546) = 6
LCM(540,546) = ( 540 × 546) / 6
LCM(540,546) = 294840 / 6
LCM(540,546) = 49140

Properties of LCM 540 and 546

(i) The LCM of 546 and 540 is associative

LCM of 540 and 546 = LCM of 546 and 540

Related Least Common Multiples of 540

Related Least Common Multiples of 546

Frequently Asked Questions on LCM of 540 and 546

1. What is the LCM of 540 and 546?

Answer: LCM of 540 and 546 is 49140.

2. What are the Factors of 540?

Answer: Factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540. There are 24 integers that are factors of 540. The greatest factor of 540 is 540.

3. 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.

4. How to Find the LCM of 540 and 546?

Answer:

Least Common Multiple of 540 and 546 = 49140

Step 1: Find the prime factorization of 540

540 = 2 x 2 x 3 x 3 x 3 x 5

Step 2: Find the prime factorization of 546

546 = 2 x 3 x 7 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 = 49140 = 2 x 2 x 3 x 3 x 3 x 5 x 7 x 13

Step 4: Therefore, the least common multiple of 540 and 546 is 49140.