What is the Least Common Multiple of 46200 and 46214?

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 46200 and 46214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 46200 and 46214, than apply into the LCM equation.

GCF(46200,46214) = 14
LCM(46200,46214) = ( 46200 × 46214) / 14
LCM(46200,46214) = 2135086800 / 14
LCM(46200,46214) = 152506200

Least Common Multiple (LCM) of 46200 and 46214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 46200 and 46214. First we will calculate the prime factors of 46200 and 46214.

Prime Factorization of 46200

Prime Factorization of 46214

Now multiplying the highest exponent prime factors to calculate the LCM of 46200 and 46214.

LCM(46200,46214) = 2³ × 3¹ × 5² × 7¹ × 11¹ × 3301¹
LCM(46200,46214) = 152506200