What is the Least Common Multiple of 48100 and 48112?

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 48100 and 48112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48100 and 48112, than apply into the LCM equation.

GCF(48100,48112) = 4
LCM(48100,48112) = ( 48100 × 48112) / 4
LCM(48100,48112) = 2314187200 / 4
LCM(48100,48112) = 578546800

Least Common Multiple (LCM) of 48100 and 48112 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 48100 and 48112. First we will calculate the prime factors of 48100 and 48112.

Prime Factorization of 48100

Prime Factorization of 48112

Now multiplying the highest exponent prime factors to calculate the LCM of 48100 and 48112.

LCM(48100,48112) = 2⁴ × 5² × 13¹ × 37¹ × 31¹ × 97¹
LCM(48100,48112) = 578546800