What is the Least Common Multiple of 32204 and 32214?

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 32204 and 32214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32204 and 32214, than apply into the LCM equation.

GCF(32204,32214) = 2
LCM(32204,32214) = ( 32204 × 32214) / 2
LCM(32204,32214) = 1037419656 / 2
LCM(32204,32214) = 518709828

Least Common Multiple (LCM) of 32204 and 32214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32204 and 32214. First we will calculate the prime factors of 32204 and 32214.

Prime Factorization of 32204

Prime Factorization of 32214

Now multiplying the highest exponent prime factors to calculate the LCM of 32204 and 32214.

LCM(32204,32214) = 2² × 83¹ × 97¹ × 3¹ × 7¹ × 13¹ × 59¹
LCM(32204,32214) = 518709828