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What is the Least Common Multiple of 1298 and 1305?

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 1298 and 1305 is 1693890.

LCM(1298,1305) = 1693890

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Least Common Multiple of 1298 and 1305 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1298 and 1305, than apply into the LCM equation.

GCF(1298,1305) = 1
LCM(1298,1305) = ( 1298 × 1305) / 1
LCM(1298,1305) = 1693890 / 1
LCM(1298,1305) = 1693890

Least Common Multiple (LCM) of 1298 and 1305 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1298 and 1305. First we will calculate the prime factors of 1298 and 1305.

Prime Factorization of 1298

Prime factors of 1298 are 2, 11, 59. Prime factorization of 1298 in exponential form is:

1298 = 21 × 111 × 591

Prime Factorization of 1305

Prime factors of 1305 are 3, 5, 29. Prime factorization of 1305 in exponential form is:

1305 = 32 × 51 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 1298 and 1305.

LCM(1298,1305) = 21 × 111 × 591 × 32 × 51 × 291
LCM(1298,1305) = 1693890