What is the Least Common Multiple of 10224 and 10230?

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 10224 and 10230 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10224 and 10230, than apply into the LCM equation.

GCF(10224,10230) = 6
LCM(10224,10230) = ( 10224 × 10230) / 6
LCM(10224,10230) = 104591520 / 6
LCM(10224,10230) = 17431920

Least Common Multiple (LCM) of 10224 and 10230 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10224 and 10230. First we will calculate the prime factors of 10224 and 10230.

Prime Factorization of 10224

Prime Factorization of 10230

Now multiplying the highest exponent prime factors to calculate the LCM of 10224 and 10230.

LCM(10224,10230) = 2⁴ × 3² × 71¹ × 5¹ × 11¹ × 31¹
LCM(10224,10230) = 17431920