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Least Common Multiple of 30 and 45

Least common multiple (LCM) of 30 and 45 is 90.

LCM(30,45) = 90

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.

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Least Common Multiple of 30 and 45 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30 and 45, than apply into the LCM equation.

GCF(30,45) = 15
LCM(30,45) = ( 30 × 45) / 15
LCM(30,45) = 1350 / 15
LCM(30,45) = 90

Least Common Multiple (LCM) of 30 and 45 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 45. First we will calculate the prime factors of 30 and 45.

Prime Factorization of 30

Prime factors of 30 are 2, 3, 5. Prime factorization of 30 in exponential form is:

30 = 21 × 31 × 51

Prime Factorization of 45

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

45 = 32 × 51

Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 45.

LCM(30,45) = 21 × 32 × 51
LCM(30,45) = 90

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