What is the Least Common Multiple of 46560 and 46575?

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 46560 and 46575 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 46560 and 46575, than apply into the LCM equation.

GCF(46560,46575) = 15
LCM(46560,46575) = ( 46560 × 46575) / 15
LCM(46560,46575) = 2168532000 / 15
LCM(46560,46575) = 144568800

Least Common Multiple (LCM) of 46560 and 46575 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 46560 and 46575. First we will calculate the prime factors of 46560 and 46575.

Prime Factorization of 46560

Prime Factorization of 46575

Now multiplying the highest exponent prime factors to calculate the LCM of 46560 and 46575.

LCM(46560,46575) = 2⁵ × 3⁴ × 5² × 97¹ × 23¹
LCM(46560,46575) = 144568800