What is the Least Common Multiple of 38496 and 38514?

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 38496 and 38514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38496 and 38514, than apply into the LCM equation.

GCF(38496,38514) = 6
LCM(38496,38514) = ( 38496 × 38514) / 6
LCM(38496,38514) = 1482634944 / 6
LCM(38496,38514) = 247105824

Least Common Multiple (LCM) of 38496 and 38514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38496 and 38514. First we will calculate the prime factors of 38496 and 38514.

Prime Factorization of 38496

Prime Factorization of 38514

Now multiplying the highest exponent prime factors to calculate the LCM of 38496 and 38514.

LCM(38496,38514) = 2⁵ × 3¹ × 401¹ × 7² × 131¹
LCM(38496,38514) = 247105824