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What is the Least Common Multiple of 46656 and 46668?

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 (LCM) of 46656 and 46668 is 181445184.

LCM(46656,46668) = 181445184

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Least Common Multiple of 46656 and 46668 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 46668, than apply into the LCM equation.

GCF(46656,46668) = 12
LCM(46656,46668) = ( 46656 × 46668) / 12
LCM(46656,46668) = 2177342208 / 12
LCM(46656,46668) = 181445184

Least Common Multiple (LCM) of 46656 and 46668 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 46656 and 46668. First we will calculate the prime factors of 46656 and 46668.

Prime Factorization of 46656

Prime factors of 46656 are 2, 3. Prime factorization of 46656 in exponential form is:

46656 = 26 × 36

Prime Factorization of 46668

Prime factors of 46668 are 2, 3, 3889. Prime factorization of 46668 in exponential form is:

46668 = 22 × 31 × 38891

Now multiplying the highest exponent prime factors to calculate the LCM of 46656 and 46668.

LCM(46656,46668) = 26 × 36 × 38891
LCM(46656,46668) = 181445184