What is the Least Common Multiple of 33408 and 33414?

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 33408 and 33414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33408 and 33414, than apply into the LCM equation.

GCF(33408,33414) = 6
LCM(33408,33414) = ( 33408 × 33414) / 6
LCM(33408,33414) = 1116294912 / 6
LCM(33408,33414) = 186049152

Least Common Multiple (LCM) of 33408 and 33414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33408 and 33414. First we will calculate the prime factors of 33408 and 33414.

Prime Factorization of 33408

Prime Factorization of 33414

Now multiplying the highest exponent prime factors to calculate the LCM of 33408 and 33414.

LCM(33408,33414) = 2⁷ × 3² × 29¹ × 5569¹
LCM(33408,33414) = 186049152