What is the Least Common Multiple of 30045 and 30054?

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 30045 and 30054 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30045 and 30054, than apply into the LCM equation.

GCF(30045,30054) = 3
LCM(30045,30054) = ( 30045 × 30054) / 3
LCM(30045,30054) = 902972430 / 3
LCM(30045,30054) = 300990810

Least Common Multiple (LCM) of 30045 and 30054 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30045 and 30054. First we will calculate the prime factors of 30045 and 30054.

Prime Factorization of 30045

Prime Factorization of 30054

Now multiplying the highest exponent prime factors to calculate the LCM of 30045 and 30054.

LCM(30045,30054) = 3¹ × 5¹ × 2003¹ × 2¹ × 5009¹
LCM(30045,30054) = 300990810