What is the Least Common Multiple of 46656 and 46667?

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 46656 and 46667 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 46656 and 46667, than apply into the LCM equation.

GCF(46656,46667) = 1
LCM(46656,46667) = ( 46656 × 46667) / 1
LCM(46656,46667) = 2177295552 / 1
LCM(46656,46667) = 2177295552

Least Common Multiple (LCM) of 46656 and 46667 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 46656 and 46667. First we will calculate the prime factors of 46656 and 46667.

Prime Factorization of 46656

Prime Factorization of 46667

Now multiplying the highest exponent prime factors to calculate the LCM of 46656 and 46667.

LCM(46656,46667) = 2⁶ × 3⁶ × 23¹ × 2029¹
LCM(46656,46667) = 2177295552