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What is the Least Common Multiple of 45 and 54?

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 45 and 54 is 270.

LCM(45,54) = 270

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Least Common Multiple of 45 and 54 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45 and 54, than apply into the LCM equation.

GCF(45,54) = 9
LCM(45,54) = ( 45 × 54) / 9
LCM(45,54) = 2430 / 9
LCM(45,54) = 270

Least Common Multiple (LCM) of 45 and 54 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45 and 54. First we will calculate the prime factors of 45 and 54.

Prime Factorization of 45

Prime factors of 45 are 3, 5. Prime factorization of 45 in exponential form is:

45 = 32 × 51

Prime Factorization of 54

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

54 = 21 × 33

Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 54.

LCM(45,54) = 33 × 51 × 21
LCM(45,54) = 270

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