What is the Least Common Multiple of 38900 and 38912?

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 38900 and 38912 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38900 and 38912, than apply into the LCM equation.

GCF(38900,38912) = 4
LCM(38900,38912) = ( 38900 × 38912) / 4
LCM(38900,38912) = 1513676800 / 4
LCM(38900,38912) = 378419200

Least Common Multiple (LCM) of 38900 and 38912 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38900 and 38912. First we will calculate the prime factors of 38900 and 38912.

Prime Factorization of 38900

Prime Factorization of 38912

Now multiplying the highest exponent prime factors to calculate the LCM of 38900 and 38912.

LCM(38900,38912) = 2¹¹ × 5² × 389¹ × 19¹
LCM(38900,38912) = 378419200