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What is the Least Common Multiple of 7565 and 7578?

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 7565 and 7578 is 57327570.

LCM(7565,7578) = 57327570

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Least Common Multiple of 7565 and 7578 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7565 and 7578, than apply into the LCM equation.

GCF(7565,7578) = 1
LCM(7565,7578) = ( 7565 × 7578) / 1
LCM(7565,7578) = 57327570 / 1
LCM(7565,7578) = 57327570

Least Common Multiple (LCM) of 7565 and 7578 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7565 and 7578. First we will calculate the prime factors of 7565 and 7578.

Prime Factorization of 7565

Prime factors of 7565 are 5, 17, 89. Prime factorization of 7565 in exponential form is:

7565 = 51 × 171 × 891

Prime Factorization of 7578

Prime factors of 7578 are 2, 3, 421. Prime factorization of 7578 in exponential form is:

7578 = 21 × 32 × 4211

Now multiplying the highest exponent prime factors to calculate the LCM of 7565 and 7578.

LCM(7565,7578) = 51 × 171 × 891 × 21 × 32 × 4211
LCM(7565,7578) = 57327570