What is the Least Common Multiple of 53208 and 53214?

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 53208 and 53214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 53208 and 53214, than apply into the LCM equation.

GCF(53208,53214) = 6
LCM(53208,53214) = ( 53208 × 53214) / 6
LCM(53208,53214) = 2831410512 / 6
LCM(53208,53214) = 471901752

Least Common Multiple (LCM) of 53208 and 53214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 53208 and 53214. First we will calculate the prime factors of 53208 and 53214.

Prime Factorization of 53208

Prime Factorization of 53214

Now multiplying the highest exponent prime factors to calculate the LCM of 53208 and 53214.

LCM(53208,53214) = 2³ × 3² × 739¹ × 7² × 181¹
LCM(53208,53214) = 471901752