What is the Least Common Multiple of 5208 and 5223?

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 5223 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 5223, than apply into the LCM equation.

GCF(5208,5223) = 3
LCM(5208,5223) = ( 5208 × 5223) / 3
LCM(5208,5223) = 27201384 / 3
LCM(5208,5223) = 9067128

Least Common Multiple (LCM) of 5208 and 5223 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5208 and 5223. First we will calculate the prime factors of 5208 and 5223.

Prime Factorization of 5208

Prime Factorization of 5223

Now multiplying the highest exponent prime factors to calculate the LCM of 5208 and 5223.

LCM(5208,5223) = 2³ × 3¹ × 7¹ × 31¹ × 1741¹
LCM(5208,5223) = 9067128