What is the Least Common Multiple of 34496 and 34514?

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 34496 and 34514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34496 and 34514, than apply into the LCM equation.

GCF(34496,34514) = 2
LCM(34496,34514) = ( 34496 × 34514) / 2
LCM(34496,34514) = 1190594944 / 2
LCM(34496,34514) = 595297472

Least Common Multiple (LCM) of 34496 and 34514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34496 and 34514. First we will calculate the prime factors of 34496 and 34514.

Prime Factorization of 34496

Prime Factorization of 34514

Now multiplying the highest exponent prime factors to calculate the LCM of 34496 and 34514.

LCM(34496,34514) = 2⁶ × 7² × 11¹ × 17257¹
LCM(34496,34514) = 595297472