What is the Least Common Multiple of 5200 and 5214?

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 5200 and 5214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5200 and 5214, than apply into the LCM equation.

GCF(5200,5214) = 2
LCM(5200,5214) = ( 5200 × 5214) / 2
LCM(5200,5214) = 27112800 / 2
LCM(5200,5214) = 13556400

Least Common Multiple (LCM) of 5200 and 5214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5200 and 5214. First we will calculate the prime factors of 5200 and 5214.

Prime Factorization of 5200

Prime Factorization of 5214

Now multiplying the highest exponent prime factors to calculate the LCM of 5200 and 5214.

LCM(5200,5214) = 2⁴ × 5² × 13¹ × 3¹ × 11¹ × 79¹
LCM(5200,5214) = 13556400