What is the Least Common Multiple of 46080 and 46090?

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 46090 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 46090, than apply into the LCM equation.

GCF(46080,46090) = 10
LCM(46080,46090) = ( 46080 × 46090) / 10
LCM(46080,46090) = 2123827200 / 10
LCM(46080,46090) = 212382720

Least Common Multiple (LCM) of 46080 and 46090 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 46080 and 46090. First we will calculate the prime factors of 46080 and 46090.

Prime Factorization of 46080

Prime Factorization of 46090

Now multiplying the highest exponent prime factors to calculate the LCM of 46080 and 46090.

LCM(46080,46090) = 2¹⁰ × 3² × 5¹ × 11¹ × 419¹
LCM(46080,46090) = 212382720