What is the Least Common Multiple of 10304 and 10315?

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 10304 and 10315 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10304 and 10315, than apply into the LCM equation.

GCF(10304,10315) = 1
LCM(10304,10315) = ( 10304 × 10315) / 1
LCM(10304,10315) = 106285760 / 1
LCM(10304,10315) = 106285760

Least Common Multiple (LCM) of 10304 and 10315 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10304 and 10315. First we will calculate the prime factors of 10304 and 10315.

Prime Factorization of 10304

Prime Factorization of 10315

Now multiplying the highest exponent prime factors to calculate the LCM of 10304 and 10315.

LCM(10304,10315) = 2⁶ × 7¹ × 23¹ × 5¹ × 2063¹
LCM(10304,10315) = 106285760