What is the Least Common Multiple of 782 and 800?

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 782 and 800 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 782 and 800, than apply into the LCM equation.

GCF(782,800) = 2
LCM(782,800) = ( 782 × 800) / 2
LCM(782,800) = 625600 / 2
LCM(782,800) = 312800

Least Common Multiple (LCM) of 782 and 800 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 782 and 800. First we will calculate the prime factors of 782 and 800.

Prime Factorization of 782

Prime Factorization of 800

Now multiplying the highest exponent prime factors to calculate the LCM of 782 and 800.

LCM(782,800) = 2⁵ × 17¹ × 23¹ × 5²
LCM(782,800) = 312800