What is the Least Common Multiple of 17205 and 17214?

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 17205 and 17214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17205 and 17214, than apply into the LCM equation.

GCF(17205,17214) = 3
LCM(17205,17214) = ( 17205 × 17214) / 3
LCM(17205,17214) = 296166870 / 3
LCM(17205,17214) = 98722290

Least Common Multiple (LCM) of 17205 and 17214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17205 and 17214. First we will calculate the prime factors of 17205 and 17214.

Prime Factorization of 17205

Prime Factorization of 17214

Now multiplying the highest exponent prime factors to calculate the LCM of 17205 and 17214.

LCM(17205,17214) = 3¹ × 5¹ × 31¹ × 37¹ × 2¹ × 19¹ × 151¹
LCM(17205,17214) = 98722290