What is the Least Common Multiple of 10900 and 10912?

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 10900 and 10912 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10900 and 10912, than apply into the LCM equation.

GCF(10900,10912) = 4
LCM(10900,10912) = ( 10900 × 10912) / 4
LCM(10900,10912) = 118940800 / 4
LCM(10900,10912) = 29735200

Least Common Multiple (LCM) of 10900 and 10912 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10900 and 10912. First we will calculate the prime factors of 10900 and 10912.

Prime Factorization of 10900

Prime Factorization of 10912

Now multiplying the highest exponent prime factors to calculate the LCM of 10900 and 10912.

LCM(10900,10912) = 2⁵ × 5² × 109¹ × 11¹ × 31¹
LCM(10900,10912) = 29735200