What is the Least Common Multiple of 34300 and 34314?

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 34300 and 34314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34300 and 34314, than apply into the LCM equation.

GCF(34300,34314) = 14
LCM(34300,34314) = ( 34300 × 34314) / 14
LCM(34300,34314) = 1176970200 / 14
LCM(34300,34314) = 84069300

Least Common Multiple (LCM) of 34300 and 34314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34300 and 34314. First we will calculate the prime factors of 34300 and 34314.

Prime Factorization of 34300

Prime Factorization of 34314

Now multiplying the highest exponent prime factors to calculate the LCM of 34300 and 34314.

LCM(34300,34314) = 2² × 5² × 7³ × 3¹ × 19¹ × 43¹
LCM(34300,34314) = 84069300