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What is the Least Common Multiple of 1239 and 1257?

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 1239 and 1257 is 519141.

LCM(1239,1257) = 519141

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Least Common Multiple of 1239 and 1257 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1239 and 1257, than apply into the LCM equation.

GCF(1239,1257) = 3
LCM(1239,1257) = ( 1239 × 1257) / 3
LCM(1239,1257) = 1557423 / 3
LCM(1239,1257) = 519141

Least Common Multiple (LCM) of 1239 and 1257 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1239 and 1257. First we will calculate the prime factors of 1239 and 1257.

Prime Factorization of 1239

Prime factors of 1239 are 3, 7, 59. Prime factorization of 1239 in exponential form is:

1239 = 31 × 71 × 591

Prime Factorization of 1257

Prime factors of 1257 are 3, 419. Prime factorization of 1257 in exponential form is:

1257 = 31 × 4191

Now multiplying the highest exponent prime factors to calculate the LCM of 1239 and 1257.

LCM(1239,1257) = 31 × 71 × 591 × 4191
LCM(1239,1257) = 519141