What is the Least Common Multiple of 6405 and 6420?

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 6405 and 6420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6405 and 6420, than apply into the LCM equation.

GCF(6405,6420) = 15
LCM(6405,6420) = ( 6405 × 6420) / 15
LCM(6405,6420) = 41120100 / 15
LCM(6405,6420) = 2741340

Least Common Multiple (LCM) of 6405 and 6420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6405 and 6420. First we will calculate the prime factors of 6405 and 6420.

Prime Factorization of 6405

Prime Factorization of 6420

Now multiplying the highest exponent prime factors to calculate the LCM of 6405 and 6420.

LCM(6405,6420) = 3¹ × 5¹ × 7¹ × 61¹ × 2² × 107¹
LCM(6405,6420) = 2741340