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What is the Least Common Multiple of 903 and 918?

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 903 and 918 is 276318.

LCM(903,918) = 276318

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Least Common Multiple of 903 and 918 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 903 and 918, than apply into the LCM equation.

GCF(903,918) = 3
LCM(903,918) = ( 903 × 918) / 3
LCM(903,918) = 828954 / 3
LCM(903,918) = 276318

Least Common Multiple (LCM) of 903 and 918 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 903 and 918. First we will calculate the prime factors of 903 and 918.

Prime Factorization of 903

Prime factors of 903 are 3, 7, 43. Prime factorization of 903 in exponential form is:

903 = 31 × 71 × 431

Prime Factorization of 918

Prime factors of 918 are 2, 3, 17. Prime factorization of 918 in exponential form is:

918 = 21 × 33 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 903 and 918.

LCM(903,918) = 33 × 71 × 431 × 21 × 171
LCM(903,918) = 276318