What is the Least Common Multiple of 10104 and 10109?

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 10104 and 10109 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10104 and 10109, than apply into the LCM equation.

GCF(10104,10109) = 1
LCM(10104,10109) = ( 10104 × 10109) / 1
LCM(10104,10109) = 102141336 / 1
LCM(10104,10109) = 102141336

Least Common Multiple (LCM) of 10104 and 10109 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10104 and 10109. First we will calculate the prime factors of 10104 and 10109.

Prime Factorization of 10104

Prime Factorization of 10109

Now multiplying the highest exponent prime factors to calculate the LCM of 10104 and 10109.

LCM(10104,10109) = 2³ × 3¹ × 421¹ × 11¹ × 919¹
LCM(10104,10109) = 102141336