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What is the Least Common Multiple of 72 and 81?

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 72 and 81 is 648.

LCM(72,81) = 648

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Least Common Multiple of 72 and 81 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72 and 81, than apply into the LCM equation.

GCF(72,81) = 9
LCM(72,81) = ( 72 × 81) / 9
LCM(72,81) = 5832 / 9
LCM(72,81) = 648

Least Common Multiple (LCM) of 72 and 81 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72 and 81. First we will calculate the prime factors of 72 and 81.

Prime Factorization of 72

Prime factors of 72 are 2, 3. Prime factorization of 72 in exponential form is:

72 = 23 × 32

Prime Factorization of 81

Prime factors of 81 are 3. Prime factorization of 81 in exponential form is:

81 = 34

Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 81.

LCM(72,81) = 23 × 34
LCM(72,81) = 648

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