What is the Least Common Multiple of 12210 and 12224?

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 12210 and 12224 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12210 and 12224, than apply into the LCM equation.

GCF(12210,12224) = 2
LCM(12210,12224) = ( 12210 × 12224) / 2
LCM(12210,12224) = 149255040 / 2
LCM(12210,12224) = 74627520

Least Common Multiple (LCM) of 12210 and 12224 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12210 and 12224. First we will calculate the prime factors of 12210 and 12224.

Prime Factorization of 12210

Prime Factorization of 12224

Now multiplying the highest exponent prime factors to calculate the LCM of 12210 and 12224.

LCM(12210,12224) = 2⁶ × 3¹ × 5¹ × 11¹ × 37¹ × 191¹
LCM(12210,12224) = 74627520