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What is the Least Common Multiple of 30765 and 30780?

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 30765 and 30780 is 63129780.

LCM(30765,30780) = 63129780

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Least Common Multiple of 30765 and 30780 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30765 and 30780, than apply into the LCM equation.

GCF(30765,30780) = 15
LCM(30765,30780) = ( 30765 × 30780) / 15
LCM(30765,30780) = 946946700 / 15
LCM(30765,30780) = 63129780

Least Common Multiple (LCM) of 30765 and 30780 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30765 and 30780. First we will calculate the prime factors of 30765 and 30780.

Prime Factorization of 30765

Prime factors of 30765 are 3, 5, 7, 293. Prime factorization of 30765 in exponential form is:

30765 = 31 × 51 × 71 × 2931

Prime Factorization of 30780

Prime factors of 30780 are 2, 3, 5, 19. Prime factorization of 30780 in exponential form is:

30780 = 22 × 34 × 51 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 30765 and 30780.

LCM(30765,30780) = 34 × 51 × 71 × 2931 × 22 × 191
LCM(30765,30780) = 63129780