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What is the Least Common Multiple of 5754 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 5754 and 5760 is 5523840.

LCM(5754,5760) = 5523840

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Least Common Multiple of 5754 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 5754 and 5760, than apply into the LCM equation.

GCF(5754,5760) = 6
LCM(5754,5760) = ( 5754 × 5760) / 6
LCM(5754,5760) = 33143040 / 6
LCM(5754,5760) = 5523840

Least Common Multiple (LCM) of 5754 and 5760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5754 and 5760. First we will calculate the prime factors of 5754 and 5760.

Prime Factorization of 5754

Prime factors of 5754 are 2, 3, 7, 137. Prime factorization of 5754 in exponential form is:

5754 = 21 × 31 × 71 × 1371

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 5754 and 5760.

LCM(5754,5760) = 27 × 32 × 71 × 1371 × 51
LCM(5754,5760) = 5523840