What is the Least Common Multiple of 33900 and 33920?

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 33900 and 33920 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33900 and 33920, than apply into the LCM equation.

GCF(33900,33920) = 20
LCM(33900,33920) = ( 33900 × 33920) / 20
LCM(33900,33920) = 1149888000 / 20
LCM(33900,33920) = 57494400

Least Common Multiple (LCM) of 33900 and 33920 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33900 and 33920. First we will calculate the prime factors of 33900 and 33920.

Prime Factorization of 33900

Prime Factorization of 33920

Now multiplying the highest exponent prime factors to calculate the LCM of 33900 and 33920.

LCM(33900,33920) = 2⁷ × 3¹ × 5² × 113¹ × 53¹
LCM(33900,33920) = 57494400