What is the Least Common Multiple of 80400 and 80408?

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 80408 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 80408, than apply into the LCM equation.

GCF(80400,80408) = 8
LCM(80400,80408) = ( 80400 × 80408) / 8
LCM(80400,80408) = 6464803200 / 8
LCM(80400,80408) = 808100400

Least Common Multiple (LCM) of 80400 and 80408 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 80400 and 80408. First we will calculate the prime factors of 80400 and 80408.

Prime Factorization of 80400

Prime Factorization of 80408

Now multiplying the highest exponent prime factors to calculate the LCM of 80400 and 80408.

LCM(80400,80408) = 2⁴ × 3¹ × 5² × 67¹ × 19¹ × 23²
LCM(80400,80408) = 808100400