What is the Least Common Multiple of 65307 and 65312?

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 65307 and 65312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65307 and 65312, than apply into the LCM equation.

GCF(65307,65312) = 1
LCM(65307,65312) = ( 65307 × 65312) / 1
LCM(65307,65312) = 4265330784 / 1
LCM(65307,65312) = 4265330784

Least Common Multiple (LCM) of 65307 and 65312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65307 and 65312. First we will calculate the prime factors of 65307 and 65312.

Prime Factorization of 65307

Prime Factorization of 65312

Now multiplying the highest exponent prime factors to calculate the LCM of 65307 and 65312.

LCM(65307,65312) = 3¹ × 11¹ × 1979¹ × 2⁵ × 13¹ × 157¹
LCM(65307,65312) = 4265330784