What is the Least Common Multiple of 34506 and 34512?

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 34506 and 34512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34506 and 34512, than apply into the LCM equation.

GCF(34506,34512) = 6
LCM(34506,34512) = ( 34506 × 34512) / 6
LCM(34506,34512) = 1190871072 / 6
LCM(34506,34512) = 198478512

Least Common Multiple (LCM) of 34506 and 34512 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34506 and 34512. First we will calculate the prime factors of 34506 and 34512.

Prime Factorization of 34506

Prime Factorization of 34512

Now multiplying the highest exponent prime factors to calculate the LCM of 34506 and 34512.

LCM(34506,34512) = 2⁴ × 3⁵ × 71¹ × 719¹
LCM(34506,34512) = 198478512