What is the Least Common Multiple of 82674 and 82688?

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 82674 and 82688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82674 and 82688, than apply into the LCM equation.

GCF(82674,82688) = 2
LCM(82674,82688) = ( 82674 × 82688) / 2
LCM(82674,82688) = 6836147712 / 2
LCM(82674,82688) = 3418073856

Least Common Multiple (LCM) of 82674 and 82688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82674 and 82688. First we will calculate the prime factors of 82674 and 82688.

Prime Factorization of 82674

Prime Factorization of 82688

Now multiplying the highest exponent prime factors to calculate the LCM of 82674 and 82688.

LCM(82674,82688) = 2⁸ × 3³ × 1531¹ × 17¹ × 19¹
LCM(82674,82688) = 3418073856