What is the Least Common Multiple of 49500 and 49514?

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 49500 and 49514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49500 and 49514, than apply into the LCM equation.

GCF(49500,49514) = 2
LCM(49500,49514) = ( 49500 × 49514) / 2
LCM(49500,49514) = 2450943000 / 2
LCM(49500,49514) = 1225471500

Least Common Multiple (LCM) of 49500 and 49514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49500 and 49514. First we will calculate the prime factors of 49500 and 49514.

Prime Factorization of 49500

Prime Factorization of 49514

Now multiplying the highest exponent prime factors to calculate the LCM of 49500 and 49514.

LCM(49500,49514) = 2² × 3² × 5³ × 11¹ × 19¹ × 1303¹
LCM(49500,49514) = 1225471500