What is the Least Common Multiple of 54405 and 54420?

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 54405 and 54420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54405 and 54420, than apply into the LCM equation.

GCF(54405,54420) = 15
LCM(54405,54420) = ( 54405 × 54420) / 15
LCM(54405,54420) = 2960720100 / 15
LCM(54405,54420) = 197381340

Least Common Multiple (LCM) of 54405 and 54420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54405 and 54420. First we will calculate the prime factors of 54405 and 54420.

Prime Factorization of 54405

Prime Factorization of 54420

Now multiplying the highest exponent prime factors to calculate the LCM of 54405 and 54420.

LCM(54405,54420) = 3³ × 5¹ × 13¹ × 31¹ × 2² × 907¹
LCM(54405,54420) = 197381340