What is the Least Common Multiple of 10250 and 10254?

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 10250 and 10254 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10250 and 10254, than apply into the LCM equation.

GCF(10250,10254) = 2
LCM(10250,10254) = ( 10250 × 10254) / 2
LCM(10250,10254) = 105103500 / 2
LCM(10250,10254) = 52551750

Least Common Multiple (LCM) of 10250 and 10254 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10250 and 10254. First we will calculate the prime factors of 10250 and 10254.

Prime Factorization of 10250

Prime Factorization of 10254

Now multiplying the highest exponent prime factors to calculate the LCM of 10250 and 10254.

LCM(10250,10254) = 2¹ × 5³ × 41¹ × 3¹ × 1709¹
LCM(10250,10254) = 52551750