What is the Least Common Multiple of 32305 and 32312?

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 32305 and 32312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32305 and 32312, than apply into the LCM equation.

GCF(32305,32312) = 7
LCM(32305,32312) = ( 32305 × 32312) / 7
LCM(32305,32312) = 1043839160 / 7
LCM(32305,32312) = 149119880

Least Common Multiple (LCM) of 32305 and 32312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32305 and 32312. First we will calculate the prime factors of 32305 and 32312.

Prime Factorization of 32305

Prime Factorization of 32312

Now multiplying the highest exponent prime factors to calculate the LCM of 32305 and 32312.

LCM(32305,32312) = 5¹ × 7¹ × 13¹ × 71¹ × 2³ × 577¹
LCM(32305,32312) = 149119880