What is the Least Common Multiple of 46080 and 46089?

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 46080 and 46089 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 46080 and 46089, than apply into the LCM equation.

GCF(46080,46089) = 9
LCM(46080,46089) = ( 46080 × 46089) / 9
LCM(46080,46089) = 2123781120 / 9
LCM(46080,46089) = 235975680

Least Common Multiple (LCM) of 46080 and 46089 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 46080 and 46089. First we will calculate the prime factors of 46080 and 46089.

Prime Factorization of 46080

Prime Factorization of 46089

Now multiplying the highest exponent prime factors to calculate the LCM of 46080 and 46089.

LCM(46080,46089) = 2¹⁰ × 3⁴ × 5¹ × 569¹
LCM(46080,46089) = 235975680