What is the Least Common Multiple of 2085 and 2102?

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 2085 and 2102 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2085 and 2102, than apply into the LCM equation.

GCF(2085,2102) = 1
LCM(2085,2102) = ( 2085 × 2102) / 1
LCM(2085,2102) = 4382670 / 1
LCM(2085,2102) = 4382670

Least Common Multiple (LCM) of 2085 and 2102 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2085 and 2102. First we will calculate the prime factors of 2085 and 2102.

Prime Factorization of 2085

Prime Factorization of 2102

Now multiplying the highest exponent prime factors to calculate the LCM of 2085 and 2102.

LCM(2085,2102) = 3¹ × 5¹ × 139¹ × 2¹ × 1051¹
LCM(2085,2102) = 4382670