What is the Least Common Multiple of 27408 and 27414?

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 27408 and 27414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27408 and 27414, than apply into the LCM equation.

GCF(27408,27414) = 6
LCM(27408,27414) = ( 27408 × 27414) / 6
LCM(27408,27414) = 751362912 / 6
LCM(27408,27414) = 125227152

Least Common Multiple (LCM) of 27408 and 27414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27408 and 27414. First we will calculate the prime factors of 27408 and 27414.

Prime Factorization of 27408

Prime Factorization of 27414

Now multiplying the highest exponent prime factors to calculate the LCM of 27408 and 27414.

LCM(27408,27414) = 2⁴ × 3² × 571¹ × 1523¹
LCM(27408,27414) = 125227152