What is the Least Common Multiple of 10112 and 10117?

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 10112 and 10117 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10112 and 10117, than apply into the LCM equation.

GCF(10112,10117) = 1
LCM(10112,10117) = ( 10112 × 10117) / 1
LCM(10112,10117) = 102303104 / 1
LCM(10112,10117) = 102303104

Least Common Multiple (LCM) of 10112 and 10117 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10112 and 10117. First we will calculate the prime factors of 10112 and 10117.

Prime Factorization of 10112

Prime Factorization of 10117

Now multiplying the highest exponent prime factors to calculate the LCM of 10112 and 10117.

LCM(10112,10117) = 2⁷ × 79¹ × 67¹ × 151¹
LCM(10112,10117) = 102303104