What is the Least Common Multiple of 45045 and 45054?

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 45045 and 45054 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45045 and 45054, than apply into the LCM equation.

GCF(45045,45054) = 9
LCM(45045,45054) = ( 45045 × 45054) / 9
LCM(45045,45054) = 2029457430 / 9
LCM(45045,45054) = 225495270

Least Common Multiple (LCM) of 45045 and 45054 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45045 and 45054. First we will calculate the prime factors of 45045 and 45054.

Prime Factorization of 45045

Prime Factorization of 45054

Now multiplying the highest exponent prime factors to calculate the LCM of 45045 and 45054.

LCM(45045,45054) = 3² × 5¹ × 7¹ × 11¹ × 13¹ × 2¹ × 2503¹
LCM(45045,45054) = 225495270