What is the Least Common Multiple of 25700 and 25714?

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 25714 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 25714, than apply into the LCM equation.

GCF(25700,25714) = 2
LCM(25700,25714) = ( 25700 × 25714) / 2
LCM(25700,25714) = 660849800 / 2
LCM(25700,25714) = 330424900

Least Common Multiple (LCM) of 25700 and 25714 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 25700 and 25714. First we will calculate the prime factors of 25700 and 25714.

Prime Factorization of 25700

Prime Factorization of 25714

Now multiplying the highest exponent prime factors to calculate the LCM of 25700 and 25714.

LCM(25700,25714) = 2² × 5² × 257¹ × 13¹ × 23¹ × 43¹
LCM(25700,25714) = 330424900