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What is the Least Common Multiple of 1027 and 1040?

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 1027 and 1040 is 82160.

LCM(1027,1040) = 82160

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Least Common Multiple of 1027 and 1040 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1027 and 1040, than apply into the LCM equation.

GCF(1027,1040) = 13
LCM(1027,1040) = ( 1027 × 1040) / 13
LCM(1027,1040) = 1068080 / 13
LCM(1027,1040) = 82160

Least Common Multiple (LCM) of 1027 and 1040 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1027 and 1040. First we will calculate the prime factors of 1027 and 1040.

Prime Factorization of 1027

Prime factors of 1027 are 13, 79. Prime factorization of 1027 in exponential form is:

1027 = 131 × 791

Prime Factorization of 1040

Prime factors of 1040 are 2, 5, 13. Prime factorization of 1040 in exponential form is:

1040 = 24 × 51 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 1027 and 1040.

LCM(1027,1040) = 131 × 791 × 24 × 51
LCM(1027,1040) = 82160