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What is the Least Common Multiple of 90 and 105?

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 90 and 105 is 630.

LCM(90,105) = 630

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Least Common Multiple of 90 and 105 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90 and 105, than apply into the LCM equation.

GCF(90,105) = 15
LCM(90,105) = ( 90 × 105) / 15
LCM(90,105) = 9450 / 15
LCM(90,105) = 630

Least Common Multiple (LCM) of 90 and 105 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90 and 105. First we will calculate the prime factors of 90 and 105.

Prime Factorization of 90

Prime factors of 90 are 2, 3, 5. Prime factorization of 90 in exponential form is:

90 = 21 × 32 × 51

Prime Factorization of 105

Prime factors of 105 are 3, 5, 7. Prime factorization of 105 in exponential form is:

105 = 31 × 51 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 90 and 105.

LCM(90,105) = 21 × 32 × 51 × 71
LCM(90,105) = 630

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