What is the Least Common Multiple of 600 and 614?

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 600 and 614 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 600 and 614, than apply into the LCM equation.

GCF(600,614) = 2
LCM(600,614) = ( 600 × 614) / 2
LCM(600,614) = 368400 / 2
LCM(600,614) = 184200

Least Common Multiple (LCM) of 600 and 614 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 600 and 614. First we will calculate the prime factors of 600 and 614.

Prime Factorization of 600

Prime Factorization of 614

Now multiplying the highest exponent prime factors to calculate the LCM of 600 and 614.

LCM(600,614) = 2³ × 3¹ × 5² × 307¹
LCM(600,614) = 184200