What is the Least Common Multiple of 72800 and 72814?

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 72800 and 72814 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72800 and 72814, than apply into the LCM equation.

GCF(72800,72814) = 14
LCM(72800,72814) = ( 72800 × 72814) / 14
LCM(72800,72814) = 5300859200 / 14
LCM(72800,72814) = 378632800

Least Common Multiple (LCM) of 72800 and 72814 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72800 and 72814. First we will calculate the prime factors of 72800 and 72814.

Prime Factorization of 72800

Prime Factorization of 72814

Now multiplying the highest exponent prime factors to calculate the LCM of 72800 and 72814.

LCM(72800,72814) = 2⁵ × 5² × 7² × 13¹ × 743¹
LCM(72800,72814) = 378632800