What is the Least Common Multiple of 36408 and 36414?

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 36408 and 36414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 36408 and 36414, than apply into the LCM equation.

GCF(36408,36414) = 6
LCM(36408,36414) = ( 36408 × 36414) / 6
LCM(36408,36414) = 1325760912 / 6
LCM(36408,36414) = 220960152

Least Common Multiple (LCM) of 36408 and 36414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 36408 and 36414. First we will calculate the prime factors of 36408 and 36414.

Prime Factorization of 36408

Prime Factorization of 36414

Now multiplying the highest exponent prime factors to calculate the LCM of 36408 and 36414.

LCM(36408,36414) = 2³ × 3² × 37¹ × 41¹ × 7¹ × 17²
LCM(36408,36414) = 220960152