What is the Least Common Multiple of 30500 and 30512?

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 30500 and 30512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30500 and 30512, than apply into the LCM equation.

GCF(30500,30512) = 4
LCM(30500,30512) = ( 30500 × 30512) / 4
LCM(30500,30512) = 930616000 / 4
LCM(30500,30512) = 232654000

Least Common Multiple (LCM) of 30500 and 30512 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30500 and 30512. First we will calculate the prime factors of 30500 and 30512.

Prime Factorization of 30500

Prime Factorization of 30512

Now multiplying the highest exponent prime factors to calculate the LCM of 30500 and 30512.

LCM(30500,30512) = 2⁴ × 5³ × 61¹ × 1907¹
LCM(30500,30512) = 232654000