What is the Least Common Multiple of 82400 and 82414?

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 82400 and 82414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82400 and 82414, than apply into the LCM equation.

GCF(82400,82414) = 2
LCM(82400,82414) = ( 82400 × 82414) / 2
LCM(82400,82414) = 6790913600 / 2
LCM(82400,82414) = 3395456800

Least Common Multiple (LCM) of 82400 and 82414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82400 and 82414. First we will calculate the prime factors of 82400 and 82414.

Prime Factorization of 82400

Prime Factorization of 82414

Now multiplying the highest exponent prime factors to calculate the LCM of 82400 and 82414.

LCM(82400,82414) = 2⁵ × 5² × 103¹ × 89¹ × 463¹
LCM(82400,82414) = 3395456800