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Least Common Multiple of 54 and 66

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 54 and 66 is 594.

LCM(54,66) = 594

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Least Common Multiple of 54 and 66 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54 and 66, than apply into the LCM equation.

GCF(54,66) = 6
LCM(54,66) = ( 54 × 66) / 6
LCM(54,66) = 3564 / 6
LCM(54,66) = 594

Least Common Multiple (LCM) of 54 and 66 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54 and 66. First we will calculate the prime factors of 54 and 66.

Prime Factorization of 54

Prime factors of 54 are 2, 3. Prime factorization of 54 in exponential form is:

54 = 21 × 33

Prime Factorization of 66

Prime factors of 66 are 2, 3, 11. Prime factorization of 66 in exponential form is:

66 = 21 × 31 × 111

Now multiplying the highest exponent prime factors to calculate the LCM of 54 and 66.

LCM(54,66) = 21 × 33 × 111
LCM(54,66) = 594

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