What is the Least Common Multiple of 58500 and 58514?

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 58500 and 58514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 58500 and 58514, than apply into the LCM equation.

GCF(58500,58514) = 2
LCM(58500,58514) = ( 58500 × 58514) / 2
LCM(58500,58514) = 3423069000 / 2
LCM(58500,58514) = 1711534500

Least Common Multiple (LCM) of 58500 and 58514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 58500 and 58514. First we will calculate the prime factors of 58500 and 58514.

Prime Factorization of 58500

Prime Factorization of 58514

Now multiplying the highest exponent prime factors to calculate the LCM of 58500 and 58514.

LCM(58500,58514) = 2² × 3² × 5³ × 13¹ × 17¹ × 1721¹
LCM(58500,58514) = 1711534500