What is the Least Common Multiple of 42306 and 42314?

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 42314 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 42314, than apply into the LCM equation.

GCF(42306,42314) = 2
LCM(42306,42314) = ( 42306 × 42314) / 2
LCM(42306,42314) = 1790136084 / 2
LCM(42306,42314) = 895068042

Least Common Multiple (LCM) of 42306 and 42314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42306 and 42314. First we will calculate the prime factors of 42306 and 42314.

Prime Factorization of 42306

Prime Factorization of 42314

Now multiplying the highest exponent prime factors to calculate the LCM of 42306 and 42314.

LCM(42306,42314) = 2¹ × 3¹ × 11¹ × 641¹ × 21157¹
LCM(42306,42314) = 895068042