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What is the Least Common Multiple of 5749 and 5760?

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 5749 and 5760 is 33114240.

LCM(5749,5760) = 33114240

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Least Common Multiple of 5749 and 5760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5749 and 5760, than apply into the LCM equation.

GCF(5749,5760) = 1
LCM(5749,5760) = ( 5749 × 5760) / 1
LCM(5749,5760) = 33114240 / 1
LCM(5749,5760) = 33114240

Least Common Multiple (LCM) of 5749 and 5760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5749 and 5760. First we will calculate the prime factors of 5749 and 5760.

Prime Factorization of 5749

Prime factors of 5749 are 5749. Prime factorization of 5749 in exponential form is:

5749 = 57491

Prime Factorization of 5760

Prime factors of 5760 are 2, 3, 5. Prime factorization of 5760 in exponential form is:

5760 = 27 × 32 × 51

Now multiplying the highest exponent prime factors to calculate the LCM of 5749 and 5760.

LCM(5749,5760) = 57491 × 27 × 32 × 51
LCM(5749,5760) = 33114240