What is the Least Common Multiple of 82680 and 82689?

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 82680 and 82689 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82680 and 82689, than apply into the LCM equation.

GCF(82680,82689) = 3
LCM(82680,82689) = ( 82680 × 82689) / 3
LCM(82680,82689) = 6836726520 / 3
LCM(82680,82689) = 2278908840

Least Common Multiple (LCM) of 82680 and 82689 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82680 and 82689. First we will calculate the prime factors of 82680 and 82689.

Prime Factorization of 82680

Prime Factorization of 82689

Now multiplying the highest exponent prime factors to calculate the LCM of 82680 and 82689.

LCM(82680,82689) = 2³ × 3¹ × 5¹ × 13¹ × 53¹ × 43¹ × 641¹
LCM(82680,82689) = 2278908840