What is the Least Common Multiple of 78500 and 78512?

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 78500 and 78512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78500 and 78512, than apply into the LCM equation.

GCF(78500,78512) = 4
LCM(78500,78512) = ( 78500 × 78512) / 4
LCM(78500,78512) = 6163192000 / 4
LCM(78500,78512) = 1540798000

Least Common Multiple (LCM) of 78500 and 78512 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78500 and 78512. First we will calculate the prime factors of 78500 and 78512.

Prime Factorization of 78500

Prime Factorization of 78512

Now multiplying the highest exponent prime factors to calculate the LCM of 78500 and 78512.

LCM(78500,78512) = 2⁴ × 5³ × 157¹ × 7¹ × 701¹
LCM(78500,78512) = 1540798000