What is the Least Common Multiple of 78000 and 78020?

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 78000 and 78020 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78000 and 78020, than apply into the LCM equation.

GCF(78000,78020) = 20
LCM(78000,78020) = ( 78000 × 78020) / 20
LCM(78000,78020) = 6085560000 / 20
LCM(78000,78020) = 304278000

Least Common Multiple (LCM) of 78000 and 78020 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78000 and 78020. First we will calculate the prime factors of 78000 and 78020.

Prime Factorization of 78000

Prime Factorization of 78020

Now multiplying the highest exponent prime factors to calculate the LCM of 78000 and 78020.

LCM(78000,78020) = 2⁴ × 3¹ × 5³ × 13¹ × 47¹ × 83¹
LCM(78000,78020) = 304278000