What is the Least Common Multiple of 82109 and 82114?

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 82109 and 82114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82109 and 82114, than apply into the LCM equation.

GCF(82109,82114) = 1
LCM(82109,82114) = ( 82109 × 82114) / 1
LCM(82109,82114) = 6742298426 / 1
LCM(82109,82114) = 6742298426

Least Common Multiple (LCM) of 82109 and 82114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82109 and 82114. First we will calculate the prime factors of 82109 and 82114.

Prime Factorization of 82109

Prime Factorization of 82114

Now multiplying the highest exponent prime factors to calculate the LCM of 82109 and 82114.

LCM(82109,82114) = 47¹ × 1747¹ × 2¹ × 41057¹
LCM(82109,82114) = 6742298426