What is the Least Common Multiple of 77985 and 78000?

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 77985 and 78000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 77985 and 78000, than apply into the LCM equation.

GCF(77985,78000) = 15
LCM(77985,78000) = ( 77985 × 78000) / 15
LCM(77985,78000) = 6082830000 / 15
LCM(77985,78000) = 405522000

Least Common Multiple (LCM) of 77985 and 78000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 77985 and 78000. First we will calculate the prime factors of 77985 and 78000.

Prime Factorization of 77985

Prime Factorization of 78000

Now multiplying the highest exponent prime factors to calculate the LCM of 77985 and 78000.

LCM(77985,78000) = 3² × 5³ × 1733¹ × 2⁴ × 13¹
LCM(77985,78000) = 405522000