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What is the Least Common Multiple of 1293 and 1302?

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 1293 and 1302 is 561162.

LCM(1293,1302) = 561162

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Least Common Multiple of 1293 and 1302 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1293 and 1302, than apply into the LCM equation.

GCF(1293,1302) = 3
LCM(1293,1302) = ( 1293 × 1302) / 3
LCM(1293,1302) = 1683486 / 3
LCM(1293,1302) = 561162

Least Common Multiple (LCM) of 1293 and 1302 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1293 and 1302. First we will calculate the prime factors of 1293 and 1302.

Prime Factorization of 1293

Prime factors of 1293 are 3, 431. Prime factorization of 1293 in exponential form is:

1293 = 31 × 4311

Prime Factorization of 1302

Prime factors of 1302 are 2, 3, 7, 31. Prime factorization of 1302 in exponential form is:

1302 = 21 × 31 × 71 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 1293 and 1302.

LCM(1293,1302) = 31 × 4311 × 21 × 71 × 311
LCM(1293,1302) = 561162