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What is the Least Common Multiple of 30969 and 30981?

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 30969 and 30981 is 319816863.

LCM(30969,30981) = 319816863

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Least Common Multiple of 30969 and 30981 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30969 and 30981, than apply into the LCM equation.

GCF(30969,30981) = 3
LCM(30969,30981) = ( 30969 × 30981) / 3
LCM(30969,30981) = 959450589 / 3
LCM(30969,30981) = 319816863

Least Common Multiple (LCM) of 30969 and 30981 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30969 and 30981. First we will calculate the prime factors of 30969 and 30981.

Prime Factorization of 30969

Prime factors of 30969 are 3, 31, 37. Prime factorization of 30969 in exponential form is:

30969 = 33 × 311 × 371

Prime Factorization of 30981

Prime factors of 30981 are 3, 23, 449. Prime factorization of 30981 in exponential form is:

30981 = 31 × 231 × 4491

Now multiplying the highest exponent prime factors to calculate the LCM of 30969 and 30981.

LCM(30969,30981) = 33 × 311 × 371 × 231 × 4491
LCM(30969,30981) = 319816863