What is the Least Common Multiple of 522 and 542?

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 542 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 542, than apply into the LCM equation.

GCF(522,542) = 2
LCM(522,542) = ( 522 × 542) / 2
LCM(522,542) = 282924 / 2
LCM(522,542) = 141462

Least Common Multiple (LCM) of 522 and 542 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 522 and 542. First we will calculate the prime factors of 522 and 542.

Prime Factorization of 522

Prime Factorization of 542

Now multiplying the highest exponent prime factors to calculate the LCM of 522 and 542.

LCM(522,542) = 2¹ × 3² × 29¹ × 271¹
LCM(522,542) = 141462