What is the Least Common Multiple of 11500 and 11514?

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 11500 and 11514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 11500 and 11514, than apply into the LCM equation.

GCF(11500,11514) = 2
LCM(11500,11514) = ( 11500 × 11514) / 2
LCM(11500,11514) = 132411000 / 2
LCM(11500,11514) = 66205500

Least Common Multiple (LCM) of 11500 and 11514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 11500 and 11514. First we will calculate the prime factors of 11500 and 11514.

Prime Factorization of 11500

Prime Factorization of 11514

Now multiplying the highest exponent prime factors to calculate the LCM of 11500 and 11514.

LCM(11500,11514) = 2² × 5³ × 23¹ × 3¹ × 19¹ × 101¹
LCM(11500,11514) = 66205500