What is the Least Common Multiple of 20100 and 20112?

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 20100 and 20112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20100 and 20112, than apply into the LCM equation.

GCF(20100,20112) = 12
LCM(20100,20112) = ( 20100 × 20112) / 12
LCM(20100,20112) = 404251200 / 12
LCM(20100,20112) = 33687600

Least Common Multiple (LCM) of 20100 and 20112 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20100 and 20112. First we will calculate the prime factors of 20100 and 20112.

Prime Factorization of 20100

Prime Factorization of 20112

Now multiplying the highest exponent prime factors to calculate the LCM of 20100 and 20112.

LCM(20100,20112) = 2⁴ × 3¹ × 5² × 67¹ × 419¹
LCM(20100,20112) = 33687600