What is the Least Common Multiple of 49488 and 49500?

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 49488 and 49500 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49488 and 49500, than apply into the LCM equation.

GCF(49488,49500) = 12
LCM(49488,49500) = ( 49488 × 49500) / 12
LCM(49488,49500) = 2449656000 / 12
LCM(49488,49500) = 204138000

Least Common Multiple (LCM) of 49488 and 49500 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49488 and 49500. First we will calculate the prime factors of 49488 and 49500.

Prime Factorization of 49488

Prime Factorization of 49500

Now multiplying the highest exponent prime factors to calculate the LCM of 49488 and 49500.

LCM(49488,49500) = 2⁴ × 3² × 1031¹ × 5³ × 11¹
LCM(49488,49500) = 204138000