What is the Least Common Multiple of 82000 and 82014?

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 82000 and 82014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82000 and 82014, than apply into the LCM equation.

GCF(82000,82014) = 2
LCM(82000,82014) = ( 82000 × 82014) / 2
LCM(82000,82014) = 6725148000 / 2
LCM(82000,82014) = 3362574000

Least Common Multiple (LCM) of 82000 and 82014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82000 and 82014. First we will calculate the prime factors of 82000 and 82014.

Prime Factorization of 82000

Prime Factorization of 82014

Now multiplying the highest exponent prime factors to calculate the LCM of 82000 and 82014.

LCM(82000,82014) = 2⁴ × 5³ × 41¹ × 3¹ × 13669¹
LCM(82000,82014) = 3362574000