What is the Least Common Multiple of 6045 and 6054?

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 6045 and 6054 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6045 and 6054, than apply into the LCM equation.

GCF(6045,6054) = 3
LCM(6045,6054) = ( 6045 × 6054) / 3
LCM(6045,6054) = 36596430 / 3
LCM(6045,6054) = 12198810

Least Common Multiple (LCM) of 6045 and 6054 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6045 and 6054. First we will calculate the prime factors of 6045 and 6054.

Prime Factorization of 6045

Prime Factorization of 6054

Now multiplying the highest exponent prime factors to calculate the LCM of 6045 and 6054.

LCM(6045,6054) = 3¹ × 5¹ × 13¹ × 31¹ × 2¹ × 1009¹
LCM(6045,6054) = 12198810