What is the Least Common Multiple of 78400 and 78405?

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 78400 and 78405 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78400 and 78405, than apply into the LCM equation.

GCF(78400,78405) = 5
LCM(78400,78405) = ( 78400 × 78405) / 5
LCM(78400,78405) = 6146952000 / 5
LCM(78400,78405) = 1229390400

Least Common Multiple (LCM) of 78400 and 78405 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78400 and 78405. First we will calculate the prime factors of 78400 and 78405.

Prime Factorization of 78400

Prime Factorization of 78405

Now multiplying the highest exponent prime factors to calculate the LCM of 78400 and 78405.

LCM(78400,78405) = 2⁶ × 5² × 7² × 3¹ × 5227¹
LCM(78400,78405) = 1229390400