What is the Least Common Multiple of 13536 and 13542?

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 13536 and 13542 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13536 and 13542, than apply into the LCM equation.

GCF(13536,13542) = 6
LCM(13536,13542) = ( 13536 × 13542) / 6
LCM(13536,13542) = 183304512 / 6
LCM(13536,13542) = 30550752

Least Common Multiple (LCM) of 13536 and 13542 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13536 and 13542. First we will calculate the prime factors of 13536 and 13542.

Prime Factorization of 13536

Prime Factorization of 13542

Now multiplying the highest exponent prime factors to calculate the LCM of 13536 and 13542.

LCM(13536,13542) = 2⁵ × 3² × 47¹ × 37¹ × 61¹
LCM(13536,13542) = 30550752