What is the Least Common Multiple of 10125 and 10142?

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 10125 and 10142 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10125 and 10142, than apply into the LCM equation.

GCF(10125,10142) = 1
LCM(10125,10142) = ( 10125 × 10142) / 1
LCM(10125,10142) = 102687750 / 1
LCM(10125,10142) = 102687750

Least Common Multiple (LCM) of 10125 and 10142 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10125 and 10142. First we will calculate the prime factors of 10125 and 10142.

Prime Factorization of 10125

Prime Factorization of 10142

Now multiplying the highest exponent prime factors to calculate the LCM of 10125 and 10142.

LCM(10125,10142) = 3⁴ × 5³ × 2¹ × 11¹ × 461¹
LCM(10125,10142) = 102687750