What is the Least Common Multiple of 14496 and 14514?

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 14496 and 14514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14496 and 14514, than apply into the LCM equation.

GCF(14496,14514) = 6
LCM(14496,14514) = ( 14496 × 14514) / 6
LCM(14496,14514) = 210394944 / 6
LCM(14496,14514) = 35065824

Least Common Multiple (LCM) of 14496 and 14514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14496 and 14514. First we will calculate the prime factors of 14496 and 14514.

Prime Factorization of 14496

Prime Factorization of 14514

Now multiplying the highest exponent prime factors to calculate the LCM of 14496 and 14514.

LCM(14496,14514) = 2⁵ × 3¹ × 151¹ × 41¹ × 59¹
LCM(14496,14514) = 35065824