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Least Common Multiple of 900 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 900 and 918 is 45900.

LCM(900,918) = 45900

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Least Common Multiple of 900 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 900 and 918, than apply into the LCM equation.

GCF(900,918) = 18
LCM(900,918) = ( 900 × 918) / 18
LCM(900,918) = 826200 / 18
LCM(900,918) = 45900

Least Common Multiple (LCM) of 900 and 918 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 900 and 918. First we will calculate the prime factors of 900 and 918.

Prime Factorization of 900

Prime factors of 900 are 2, 3, 5. Prime factorization of 900 in exponential form is:

900 = 22 × 32 × 52

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 900 and 918.

LCM(900,918) = 22 × 33 × 52 × 171
LCM(900,918) = 45900

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