What is the Least Common Multiple of 5208 and 5219?

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 5208 and 5219 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5208 and 5219, than apply into the LCM equation.

GCF(5208,5219) = 1
LCM(5208,5219) = ( 5208 × 5219) / 1
LCM(5208,5219) = 27180552 / 1
LCM(5208,5219) = 27180552

Least Common Multiple (LCM) of 5208 and 5219 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5208 and 5219. First we will calculate the prime factors of 5208 and 5219.

Prime Factorization of 5208

Prime Factorization of 5219

Now multiplying the highest exponent prime factors to calculate the LCM of 5208 and 5219.

LCM(5208,5219) = 2³ × 3¹ × 7¹ × 31¹ × 17¹ × 307¹
LCM(5208,5219) = 27180552