What is the Least Common Multiple of 33500 and 33504?

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 33500 and 33504 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33500 and 33504, than apply into the LCM equation.

GCF(33500,33504) = 4
LCM(33500,33504) = ( 33500 × 33504) / 4
LCM(33500,33504) = 1122384000 / 4
LCM(33500,33504) = 280596000

Least Common Multiple (LCM) of 33500 and 33504 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33500 and 33504. First we will calculate the prime factors of 33500 and 33504.

Prime Factorization of 33500

Prime Factorization of 33504

Now multiplying the highest exponent prime factors to calculate the LCM of 33500 and 33504.

LCM(33500,33504) = 2⁵ × 5³ × 67¹ × 3¹ × 349¹
LCM(33500,33504) = 280596000