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What is the Least Common Multiple of 1292 and 1311?

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 1292 and 1311 is 89148.

LCM(1292,1311) = 89148

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Least Common Multiple of 1292 and 1311 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1292 and 1311, than apply into the LCM equation.

GCF(1292,1311) = 19
LCM(1292,1311) = ( 1292 × 1311) / 19
LCM(1292,1311) = 1693812 / 19
LCM(1292,1311) = 89148

Least Common Multiple (LCM) of 1292 and 1311 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1292 and 1311. First we will calculate the prime factors of 1292 and 1311.

Prime Factorization of 1292

Prime factors of 1292 are 2, 17, 19. Prime factorization of 1292 in exponential form is:

1292 = 22 × 171 × 191

Prime Factorization of 1311

Prime factors of 1311 are 3, 19, 23. Prime factorization of 1311 in exponential form is:

1311 = 31 × 191 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 1292 and 1311.

LCM(1292,1311) = 22 × 171 × 191 × 31 × 231
LCM(1292,1311) = 89148