What is the Least Common Multiple of 80400 and 80415?

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 80400 and 80415 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 80400 and 80415, than apply into the LCM equation.

GCF(80400,80415) = 15
LCM(80400,80415) = ( 80400 × 80415) / 15
LCM(80400,80415) = 6465366000 / 15
LCM(80400,80415) = 431024400

Least Common Multiple (LCM) of 80400 and 80415 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 80400 and 80415. First we will calculate the prime factors of 80400 and 80415.

Prime Factorization of 80400

Prime Factorization of 80415

Now multiplying the highest exponent prime factors to calculate the LCM of 80400 and 80415.

LCM(80400,80415) = 2⁴ × 3² × 5² × 67¹ × 1787¹
LCM(80400,80415) = 431024400