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What is the Least Common Multiple of 5972 and 5985?

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 5972 and 5985 is 35742420.

LCM(5972,5985) = 35742420

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Least Common Multiple of 5972 and 5985 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5972 and 5985, than apply into the LCM equation.

GCF(5972,5985) = 1
LCM(5972,5985) = ( 5972 × 5985) / 1
LCM(5972,5985) = 35742420 / 1
LCM(5972,5985) = 35742420

Least Common Multiple (LCM) of 5972 and 5985 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5972 and 5985. First we will calculate the prime factors of 5972 and 5985.

Prime Factorization of 5972

Prime factors of 5972 are 2, 1493. Prime factorization of 5972 in exponential form is:

5972 = 22 × 14931

Prime Factorization of 5985

Prime factors of 5985 are 3, 5, 7, 19. Prime factorization of 5985 in exponential form is:

5985 = 32 × 51 × 71 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 5972 and 5985.

LCM(5972,5985) = 22 × 14931 × 32 × 51 × 71 × 191
LCM(5972,5985) = 35742420