What is the Least Common Multiple of 82400 and 82419?

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 82419 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 82419, than apply into the LCM equation.

GCF(82400,82419) = 1
LCM(82400,82419) = ( 82400 × 82419) / 1
LCM(82400,82419) = 6791325600 / 1
LCM(82400,82419) = 6791325600

Least Common Multiple (LCM) of 82400 and 82419 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82400 and 82419. First we will calculate the prime factors of 82400 and 82419.

Prime Factorization of 82400

Prime Factorization of 82419

Now multiplying the highest exponent prime factors to calculate the LCM of 82400 and 82419.

LCM(82400,82419) = 2⁵ × 5² × 103¹ × 3¹ × 83¹ × 331¹
LCM(82400,82419) = 6791325600