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What is the Least Common Multiple of 30772 and 30784?

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 30772 and 30784 is 236821312.

LCM(30772,30784) = 236821312

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Least Common Multiple of 30772 and 30784 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30772 and 30784, than apply into the LCM equation.

GCF(30772,30784) = 4
LCM(30772,30784) = ( 30772 × 30784) / 4
LCM(30772,30784) = 947285248 / 4
LCM(30772,30784) = 236821312

Least Common Multiple (LCM) of 30772 and 30784 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30772 and 30784. First we will calculate the prime factors of 30772 and 30784.

Prime Factorization of 30772

Prime factors of 30772 are 2, 7, 157. Prime factorization of 30772 in exponential form is:

30772 = 22 × 72 × 1571

Prime Factorization of 30784

Prime factors of 30784 are 2, 13, 37. Prime factorization of 30784 in exponential form is:

30784 = 26 × 131 × 371

Now multiplying the highest exponent prime factors to calculate the LCM of 30772 and 30784.

LCM(30772,30784) = 26 × 72 × 1571 × 131 × 371
LCM(30772,30784) = 236821312