What is the Least Common Multiple of 82100 and 82109?

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 82100 and 82109 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82100 and 82109, than apply into the LCM equation.

GCF(82100,82109) = 1
LCM(82100,82109) = ( 82100 × 82109) / 1
LCM(82100,82109) = 6741148900 / 1
LCM(82100,82109) = 6741148900

Least Common Multiple (LCM) of 82100 and 82109 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82100 and 82109. First we will calculate the prime factors of 82100 and 82109.

Prime Factorization of 82100

Prime Factorization of 82109

Now multiplying the highest exponent prime factors to calculate the LCM of 82100 and 82109.

LCM(82100,82109) = 2² × 5² × 821¹ × 47¹ × 1747¹
LCM(82100,82109) = 6741148900