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What is the Least Common Multiple of 43770 and 43776?

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 43770 and 43776 is 319345920.

LCM(43770,43776) = 319345920

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Least Common Multiple of 43770 and 43776 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 43770 and 43776, than apply into the LCM equation.

GCF(43770,43776) = 6
LCM(43770,43776) = ( 43770 × 43776) / 6
LCM(43770,43776) = 1916075520 / 6
LCM(43770,43776) = 319345920

Least Common Multiple (LCM) of 43770 and 43776 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 43770 and 43776. First we will calculate the prime factors of 43770 and 43776.

Prime Factorization of 43770

Prime factors of 43770 are 2, 3, 5, 1459. Prime factorization of 43770 in exponential form is:

43770 = 21 × 31 × 51 × 14591

Prime Factorization of 43776

Prime factors of 43776 are 2, 3, 19. Prime factorization of 43776 in exponential form is:

43776 = 28 × 32 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 43770 and 43776.

LCM(43770,43776) = 28 × 32 × 51 × 14591 × 191
LCM(43770,43776) = 319345920