What is the Least Common Multiple of 30400 and 30414?

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 30400 and 30414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30400 and 30414, than apply into the LCM equation.

GCF(30400,30414) = 2
LCM(30400,30414) = ( 30400 × 30414) / 2
LCM(30400,30414) = 924585600 / 2
LCM(30400,30414) = 462292800

Least Common Multiple (LCM) of 30400 and 30414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30400 and 30414. First we will calculate the prime factors of 30400 and 30414.

Prime Factorization of 30400

Prime Factorization of 30414

Now multiplying the highest exponent prime factors to calculate the LCM of 30400 and 30414.

LCM(30400,30414) = 2⁶ × 5² × 19¹ × 3¹ × 37¹ × 137¹
LCM(30400,30414) = 462292800