What is the Least Common Multiple of 46380 and 46400?

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 46380 and 46400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 46380 and 46400, than apply into the LCM equation.

GCF(46380,46400) = 20
LCM(46380,46400) = ( 46380 × 46400) / 20
LCM(46380,46400) = 2152032000 / 20
LCM(46380,46400) = 107601600

Least Common Multiple (LCM) of 46380 and 46400 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 46380 and 46400. First we will calculate the prime factors of 46380 and 46400.

Prime Factorization of 46380

Prime Factorization of 46400

Now multiplying the highest exponent prime factors to calculate the LCM of 46380 and 46400.

LCM(46380,46400) = 2⁶ × 3¹ × 5² × 773¹ × 29¹
LCM(46380,46400) = 107601600