What is the Least Common Multiple of 57408 and 57414?

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 57408 and 57414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57408 and 57414, than apply into the LCM equation.

GCF(57408,57414) = 6
LCM(57408,57414) = ( 57408 × 57414) / 6
LCM(57408,57414) = 3296022912 / 6
LCM(57408,57414) = 549337152

Least Common Multiple (LCM) of 57408 and 57414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57408 and 57414. First we will calculate the prime factors of 57408 and 57414.

Prime Factorization of 57408

Prime Factorization of 57414

Now multiplying the highest exponent prime factors to calculate the LCM of 57408 and 57414.

LCM(57408,57414) = 2⁶ × 3¹ × 13¹ × 23¹ × 7¹ × 1367¹
LCM(57408,57414) = 549337152