What is the Least Common Multiple of 34104 and 34112?

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 34104 and 34112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34104 and 34112, than apply into the LCM equation.

GCF(34104,34112) = 8
LCM(34104,34112) = ( 34104 × 34112) / 8
LCM(34104,34112) = 1163355648 / 8
LCM(34104,34112) = 145419456

Least Common Multiple (LCM) of 34104 and 34112 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34104 and 34112. First we will calculate the prime factors of 34104 and 34112.

Prime Factorization of 34104

Prime Factorization of 34112

Now multiplying the highest exponent prime factors to calculate the LCM of 34104 and 34112.

LCM(34104,34112) = 2⁶ × 3¹ × 7² × 29¹ × 13¹ × 41¹
LCM(34104,34112) = 145419456