What is the Least Common Multiple of 65400 and 65420?

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 65400 and 65420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65400 and 65420, than apply into the LCM equation.

GCF(65400,65420) = 20
LCM(65400,65420) = ( 65400 × 65420) / 20
LCM(65400,65420) = 4278468000 / 20
LCM(65400,65420) = 213923400

Least Common Multiple (LCM) of 65400 and 65420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65400 and 65420. First we will calculate the prime factors of 65400 and 65420.

Prime Factorization of 65400

Prime Factorization of 65420

Now multiplying the highest exponent prime factors to calculate the LCM of 65400 and 65420.

LCM(65400,65420) = 2³ × 3¹ × 5² × 109¹ × 3271¹
LCM(65400,65420) = 213923400