What is the Least Common Multiple of 5214 and 5229?

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 5214 and 5229 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5214 and 5229, than apply into the LCM equation.

GCF(5214,5229) = 3
LCM(5214,5229) = ( 5214 × 5229) / 3
LCM(5214,5229) = 27264006 / 3
LCM(5214,5229) = 9088002

Least Common Multiple (LCM) of 5214 and 5229 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5214 and 5229. First we will calculate the prime factors of 5214 and 5229.

Prime Factorization of 5214

Prime Factorization of 5229

Now multiplying the highest exponent prime factors to calculate the LCM of 5214 and 5229.

LCM(5214,5229) = 2¹ × 3² × 11¹ × 79¹ × 7¹ × 83¹
LCM(5214,5229) = 9088002