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What is the Least Common Multiple of 1582 and 1592?

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 1582 and 1592 is 1259272.

LCM(1582,1592) = 1259272

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Least Common Multiple of 1582 and 1592 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1582 and 1592, than apply into the LCM equation.

GCF(1582,1592) = 2
LCM(1582,1592) = ( 1582 × 1592) / 2
LCM(1582,1592) = 2518544 / 2
LCM(1582,1592) = 1259272

Least Common Multiple (LCM) of 1582 and 1592 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1582 and 1592. First we will calculate the prime factors of 1582 and 1592.

Prime Factorization of 1582

Prime factors of 1582 are 2, 7, 113. Prime factorization of 1582 in exponential form is:

1582 = 21 × 71 × 1131

Prime Factorization of 1592

Prime factors of 1592 are 2, 199. Prime factorization of 1592 in exponential form is:

1592 = 23 × 1991

Now multiplying the highest exponent prime factors to calculate the LCM of 1582 and 1592.

LCM(1582,1592) = 23 × 71 × 1131 × 1991
LCM(1582,1592) = 1259272