What is the Least Common Multiple of 10230 and 10240?

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 10230 and 10240 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10230 and 10240, than apply into the LCM equation.

GCF(10230,10240) = 10
LCM(10230,10240) = ( 10230 × 10240) / 10
LCM(10230,10240) = 104755200 / 10
LCM(10230,10240) = 10475520

Least Common Multiple (LCM) of 10230 and 10240 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10230 and 10240. First we will calculate the prime factors of 10230 and 10240.

Prime Factorization of 10230

Prime Factorization of 10240

Now multiplying the highest exponent prime factors to calculate the LCM of 10230 and 10240.

LCM(10230,10240) = 2¹¹ × 3¹ × 5¹ × 11¹ × 31¹
LCM(10230,10240) = 10475520