What is the Least Common Multiple of 208 and 217?

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 208 and 217 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 208 and 217, than apply into the LCM equation.

GCF(208,217) = 1
LCM(208,217) = ( 208 × 217) / 1
LCM(208,217) = 45136 / 1
LCM(208,217) = 45136

Least Common Multiple (LCM) of 208 and 217 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 208 and 217. First we will calculate the prime factors of 208 and 217.

Prime Factorization of 208

Prime Factorization of 217

Now multiplying the highest exponent prime factors to calculate the LCM of 208 and 217.

LCM(208,217) = 2⁴ × 13¹ × 7¹ × 31¹
LCM(208,217) = 45136