What is the Least Common Multiple of 10304 and 10314?

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 10314 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 10314, than apply into the LCM equation.

GCF(10304,10314) = 2
LCM(10304,10314) = ( 10304 × 10314) / 2
LCM(10304,10314) = 106275456 / 2
LCM(10304,10314) = 53137728

Least Common Multiple (LCM) of 10304 and 10314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10304 and 10314. First we will calculate the prime factors of 10304 and 10314.

Prime Factorization of 10304

Prime Factorization of 10314

Now multiplying the highest exponent prime factors to calculate the LCM of 10304 and 10314.

LCM(10304,10314) = 2⁶ × 7¹ × 23¹ × 3³ × 191¹
LCM(10304,10314) = 53137728