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What is the Least Common Multiple of 27965 and 27974?

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 27965 and 27974 is 782292910.

LCM(27965,27974) = 782292910

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Least Common Multiple of 27965 and 27974 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27965 and 27974, than apply into the LCM equation.

GCF(27965,27974) = 1
LCM(27965,27974) = ( 27965 × 27974) / 1
LCM(27965,27974) = 782292910 / 1
LCM(27965,27974) = 782292910

Least Common Multiple (LCM) of 27965 and 27974 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27965 and 27974. First we will calculate the prime factors of 27965 and 27974.

Prime Factorization of 27965

Prime factors of 27965 are 5, 7, 17, 47. Prime factorization of 27965 in exponential form is:

27965 = 51 × 71 × 171 × 471

Prime Factorization of 27974

Prime factors of 27974 are 2, 71, 197. Prime factorization of 27974 in exponential form is:

27974 = 21 × 711 × 1971

Now multiplying the highest exponent prime factors to calculate the LCM of 27965 and 27974.

LCM(27965,27974) = 51 × 71 × 171 × 471 × 21 × 711 × 1971
LCM(27965,27974) = 782292910