What is the Least Common Multiple of 10109 and 10113?

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 10109 and 10113 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10109 and 10113, than apply into the LCM equation.

GCF(10109,10113) = 1
LCM(10109,10113) = ( 10109 × 10113) / 1
LCM(10109,10113) = 102232317 / 1
LCM(10109,10113) = 102232317

Least Common Multiple (LCM) of 10109 and 10113 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10109 and 10113. First we will calculate the prime factors of 10109 and 10113.

Prime Factorization of 10109

Prime Factorization of 10113

Now multiplying the highest exponent prime factors to calculate the LCM of 10109 and 10113.

LCM(10109,10113) = 11¹ × 919¹ × 3¹ × 3371¹
LCM(10109,10113) = 102232317