What is the Least Common Multiple of 66300 and 66314?

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 66300 and 66314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 66300 and 66314, than apply into the LCM equation.

GCF(66300,66314) = 2
LCM(66300,66314) = ( 66300 × 66314) / 2
LCM(66300,66314) = 4396618200 / 2
LCM(66300,66314) = 2198309100

Least Common Multiple (LCM) of 66300 and 66314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 66300 and 66314. First we will calculate the prime factors of 66300 and 66314.

Prime Factorization of 66300

Prime Factorization of 66314

Now multiplying the highest exponent prime factors to calculate the LCM of 66300 and 66314.

LCM(66300,66314) = 2² × 3¹ × 5² × 13¹ × 17¹ × 71¹ × 467¹
LCM(66300,66314) = 2198309100