What is the Least Common Multiple of 540 and 546?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

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

Least Common Multiple (LCM) of 540 and 546 with Primes

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

Prime Factorization of 546

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