What is the Least Common Multiple of 46800 and 46809?

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 46800 and 46809 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 46800 and 46809, than apply into the LCM equation.

GCF(46800,46809) = 9
LCM(46800,46809) = ( 46800 × 46809) / 9
LCM(46800,46809) = 2190661200 / 9
LCM(46800,46809) = 243406800

Least Common Multiple (LCM) of 46800 and 46809 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 46800 and 46809. First we will calculate the prime factors of 46800 and 46809.

Prime Factorization of 46800

Prime Factorization of 46809

Now multiplying the highest exponent prime factors to calculate the LCM of 46800 and 46809.

LCM(46800,46809) = 2⁴ × 3² × 5² × 13¹ × 7¹ × 743¹
LCM(46800,46809) = 243406800