What is the Least Common Multiple of 8100 and 8112?

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 8100 and 8112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8100 and 8112, than apply into the LCM equation.

GCF(8100,8112) = 12
LCM(8100,8112) = ( 8100 × 8112) / 12
LCM(8100,8112) = 65707200 / 12
LCM(8100,8112) = 5475600

Least Common Multiple (LCM) of 8100 and 8112 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8100 and 8112. First we will calculate the prime factors of 8100 and 8112.

Prime Factorization of 8100

Prime Factorization of 8112

Now multiplying the highest exponent prime factors to calculate the LCM of 8100 and 8112.

LCM(8100,8112) = 2⁴ × 3⁴ × 5² × 13²
LCM(8100,8112) = 5475600