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What is the Least Common Multiple of 5754 and 5772?

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 5772 is 5535348.

LCM(5754,5772) = 5535348

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Least Common Multiple of 5754 and 5772 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 5772, than apply into the LCM equation.

GCF(5754,5772) = 6
LCM(5754,5772) = ( 5754 × 5772) / 6
LCM(5754,5772) = 33212088 / 6
LCM(5754,5772) = 5535348

Least Common Multiple (LCM) of 5754 and 5772 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5754 and 5772. First we will calculate the prime factors of 5754 and 5772.

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 5772

Prime factors of 5772 are 2, 3, 13, 37. Prime factorization of 5772 in exponential form is:

5772 = 22 × 31 × 131 × 371

Now multiplying the highest exponent prime factors to calculate the LCM of 5754 and 5772.

LCM(5754,5772) = 22 × 31 × 71 × 1371 × 131 × 371
LCM(5754,5772) = 5535348