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What is the Least Common Multiple of 10767 and 10782?

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 10767 and 10782 is 38696598.

LCM(10767,10782) = 38696598

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Least Common Multiple of 10767 and 10782 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10767 and 10782, than apply into the LCM equation.

GCF(10767,10782) = 3
LCM(10767,10782) = ( 10767 × 10782) / 3
LCM(10767,10782) = 116089794 / 3
LCM(10767,10782) = 38696598

Least Common Multiple (LCM) of 10767 and 10782 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10767 and 10782. First we will calculate the prime factors of 10767 and 10782.

Prime Factorization of 10767

Prime factors of 10767 are 3, 37, 97. Prime factorization of 10767 in exponential form is:

10767 = 31 × 371 × 971

Prime Factorization of 10782

Prime factors of 10782 are 2, 3, 599. Prime factorization of 10782 in exponential form is:

10782 = 21 × 32 × 5991

Now multiplying the highest exponent prime factors to calculate the LCM of 10767 and 10782.

LCM(10767,10782) = 32 × 371 × 971 × 21 × 5991
LCM(10767,10782) = 38696598