What is the Least Common Multiple of 12400 and 12405?

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 12400 and 12405 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12400 and 12405, than apply into the LCM equation.

GCF(12400,12405) = 5
LCM(12400,12405) = ( 12400 × 12405) / 5
LCM(12400,12405) = 153822000 / 5
LCM(12400,12405) = 30764400

Least Common Multiple (LCM) of 12400 and 12405 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12400 and 12405. First we will calculate the prime factors of 12400 and 12405.

Prime Factorization of 12400

Prime Factorization of 12405

Now multiplying the highest exponent prime factors to calculate the LCM of 12400 and 12405.

LCM(12400,12405) = 2⁴ × 5² × 31¹ × 3¹ × 827¹
LCM(12400,12405) = 30764400