What is the Least Common Multiple of 25700 and 25712?

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 25700 and 25712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 25700 and 25712, than apply into the LCM equation.

GCF(25700,25712) = 4
LCM(25700,25712) = ( 25700 × 25712) / 4
LCM(25700,25712) = 660798400 / 4
LCM(25700,25712) = 165199600

Least Common Multiple (LCM) of 25700 and 25712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 25700 and 25712. First we will calculate the prime factors of 25700 and 25712.

Prime Factorization of 25700

Prime Factorization of 25712

Now multiplying the highest exponent prime factors to calculate the LCM of 25700 and 25712.

LCM(25700,25712) = 2⁴ × 5² × 257¹ × 1607¹
LCM(25700,25712) = 165199600