What is the Least Common Multiple of 24208 and 24225?

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 24208 and 24225 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 24208 and 24225, than apply into the LCM equation.

GCF(24208,24225) = 17
LCM(24208,24225) = ( 24208 × 24225) / 17
LCM(24208,24225) = 586438800 / 17
LCM(24208,24225) = 34496400

Least Common Multiple (LCM) of 24208 and 24225 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 24208 and 24225. First we will calculate the prime factors of 24208 and 24225.

Prime Factorization of 24208

Prime Factorization of 24225

Now multiplying the highest exponent prime factors to calculate the LCM of 24208 and 24225.

LCM(24208,24225) = 2⁴ × 17¹ × 89¹ × 3¹ × 5² × 19¹
LCM(24208,24225) = 34496400