What is the Least Common Multiple of 42306 and 42312?

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 42306 and 42312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42306 and 42312, than apply into the LCM equation.

GCF(42306,42312) = 6
LCM(42306,42312) = ( 42306 × 42312) / 6
LCM(42306,42312) = 1790051472 / 6
LCM(42306,42312) = 298341912

Least Common Multiple (LCM) of 42306 and 42312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42306 and 42312. First we will calculate the prime factors of 42306 and 42312.

Prime Factorization of 42306

Prime Factorization of 42312

Now multiplying the highest exponent prime factors to calculate the LCM of 42306 and 42312.

LCM(42306,42312) = 2³ × 3¹ × 11¹ × 641¹ × 41¹ × 43¹
LCM(42306,42312) = 298341912