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What is the Least Common Multiple of 42 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 42 and 54 is 378.

LCM(42,54) = 378

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Least Common Multiple of 42 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 42 and 54, than apply into the LCM equation.

GCF(42,54) = 6
LCM(42,54) = ( 42 × 54) / 6
LCM(42,54) = 2268 / 6
LCM(42,54) = 378

Least Common Multiple (LCM) of 42 and 54 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 54. First we will calculate the prime factors of 42 and 54.

Prime Factorization of 42

Prime factors of 42 are 2, 3, 7. Prime factorization of 42 in exponential form is:

42 = 21 × 31 × 71

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 42 and 54.

LCM(42,54) = 21 × 33 × 71
LCM(42,54) = 378

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