What is the Least Common Multiple of 10114 and 10123?

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 10114 and 10123 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10114 and 10123, than apply into the LCM equation.

GCF(10114,10123) = 1
LCM(10114,10123) = ( 10114 × 10123) / 1
LCM(10114,10123) = 102384022 / 1
LCM(10114,10123) = 102384022

Least Common Multiple (LCM) of 10114 and 10123 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10114 and 10123. First we will calculate the prime factors of 10114 and 10123.

Prime Factorization of 10114

Prime Factorization of 10123

Now multiplying the highest exponent prime factors to calculate the LCM of 10114 and 10123.

LCM(10114,10123) = 2¹ × 13¹ × 389¹ × 53¹ × 191¹
LCM(10114,10123) = 102384022