What is the Least Common Multiple of 67208 and 67214?

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 67208 and 67214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67208 and 67214, than apply into the LCM equation.

GCF(67208,67214) = 2
LCM(67208,67214) = ( 67208 × 67214) / 2
LCM(67208,67214) = 4517318512 / 2
LCM(67208,67214) = 2258659256

Least Common Multiple (LCM) of 67208 and 67214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67208 and 67214. First we will calculate the prime factors of 67208 and 67214.

Prime Factorization of 67208

Prime Factorization of 67214

Now multiplying the highest exponent prime factors to calculate the LCM of 67208 and 67214.

LCM(67208,67214) = 2³ × 31¹ × 271¹ × 7¹ × 4801¹
LCM(67208,67214) = 2258659256