What is the Least Common Multiple of 2085 and 2103?

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 2103 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 2103, than apply into the LCM equation.

GCF(2085,2103) = 3
LCM(2085,2103) = ( 2085 × 2103) / 3
LCM(2085,2103) = 4384755 / 3
LCM(2085,2103) = 1461585

Least Common Multiple (LCM) of 2085 and 2103 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2085 and 2103. First we will calculate the prime factors of 2085 and 2103.

Prime Factorization of 2085

Prime Factorization of 2103

Now multiplying the highest exponent prime factors to calculate the LCM of 2085 and 2103.

LCM(2085,2103) = 3¹ × 5¹ × 139¹ × 701¹
LCM(2085,2103) = 1461585