What is the Least Common Multiple of 7208 and 7214?

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 7208 and 7214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7208 and 7214, than apply into the LCM equation.

GCF(7208,7214) = 2
LCM(7208,7214) = ( 7208 × 7214) / 2
LCM(7208,7214) = 51998512 / 2
LCM(7208,7214) = 25999256

Least Common Multiple (LCM) of 7208 and 7214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7208 and 7214. First we will calculate the prime factors of 7208 and 7214.

Prime Factorization of 7208

Prime Factorization of 7214

Now multiplying the highest exponent prime factors to calculate the LCM of 7208 and 7214.

LCM(7208,7214) = 2³ × 17¹ × 53¹ × 3607¹
LCM(7208,7214) = 25999256