What is the Least Common Multiple of 10104 and 10116?

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 10116 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 10116, than apply into the LCM equation.

GCF(10104,10116) = 12
LCM(10104,10116) = ( 10104 × 10116) / 12
LCM(10104,10116) = 102212064 / 12
LCM(10104,10116) = 8517672

Least Common Multiple (LCM) of 10104 and 10116 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10104 and 10116. First we will calculate the prime factors of 10104 and 10116.

Prime Factorization of 10104

Prime Factorization of 10116

Now multiplying the highest exponent prime factors to calculate the LCM of 10104 and 10116.

LCM(10104,10116) = 2³ × 3² × 421¹ × 281¹
LCM(10104,10116) = 8517672