What is the Least Common Multiple of 10296 and 10302?

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 10296 and 10302 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10296 and 10302, than apply into the LCM equation.

GCF(10296,10302) = 6
LCM(10296,10302) = ( 10296 × 10302) / 6
LCM(10296,10302) = 106069392 / 6
LCM(10296,10302) = 17678232

Least Common Multiple (LCM) of 10296 and 10302 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10296 and 10302. First we will calculate the prime factors of 10296 and 10302.

Prime Factorization of 10296

Prime Factorization of 10302

Now multiplying the highest exponent prime factors to calculate the LCM of 10296 and 10302.

LCM(10296,10302) = 2³ × 3² × 11¹ × 13¹ × 17¹ × 101¹
LCM(10296,10302) = 17678232