What is the Least Common Multiple of 522 and 540?

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 522 and 540 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 522 and 540, than apply into the LCM equation.

GCF(522,540) = 18
LCM(522,540) = ( 522 × 540) / 18
LCM(522,540) = 281880 / 18
LCM(522,540) = 15660

Least Common Multiple (LCM) of 522 and 540 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 522 and 540. First we will calculate the prime factors of 522 and 540.

Prime Factorization of 522

Prime Factorization of 540

Now multiplying the highest exponent prime factors to calculate the LCM of 522 and 540.

LCM(522,540) = 2² × 3³ × 29¹ × 5¹
LCM(522,540) = 15660