What is the Least Common Multiple of 14208 and 14214?

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 14208 and 14214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14208 and 14214, than apply into the LCM equation.

GCF(14208,14214) = 6
LCM(14208,14214) = ( 14208 × 14214) / 6
LCM(14208,14214) = 201952512 / 6
LCM(14208,14214) = 33658752

Least Common Multiple (LCM) of 14208 and 14214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14208 and 14214. First we will calculate the prime factors of 14208 and 14214.

Prime Factorization of 14208

Prime Factorization of 14214

Now multiplying the highest exponent prime factors to calculate the LCM of 14208 and 14214.

LCM(14208,14214) = 2⁷ × 3¹ × 37¹ × 23¹ × 103¹
LCM(14208,14214) = 33658752