What is the Least Common Multiple of 38208 and 38223?

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 38208 and 38223 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38208 and 38223, than apply into the LCM equation.

GCF(38208,38223) = 3
LCM(38208,38223) = ( 38208 × 38223) / 3
LCM(38208,38223) = 1460424384 / 3
LCM(38208,38223) = 486808128

Least Common Multiple (LCM) of 38208 and 38223 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38208 and 38223. First we will calculate the prime factors of 38208 and 38223.

Prime Factorization of 38208

Prime Factorization of 38223

Now multiplying the highest exponent prime factors to calculate the LCM of 38208 and 38223.

LCM(38208,38223) = 2⁶ × 3² × 199¹ × 31¹ × 137¹
LCM(38208,38223) = 486808128