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What is the Least Common Multiple of 45355 and 45360?

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 45355 and 45360 is 411460560.

LCM(45355,45360) = 411460560

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Least Common Multiple of 45355 and 45360 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45355 and 45360, than apply into the LCM equation.

GCF(45355,45360) = 5
LCM(45355,45360) = ( 45355 × 45360) / 5
LCM(45355,45360) = 2057302800 / 5
LCM(45355,45360) = 411460560

Least Common Multiple (LCM) of 45355 and 45360 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45355 and 45360. First we will calculate the prime factors of 45355 and 45360.

Prime Factorization of 45355

Prime factors of 45355 are 5, 47, 193. Prime factorization of 45355 in exponential form is:

45355 = 51 × 471 × 1931

Prime Factorization of 45360

Prime factors of 45360 are 2, 3, 5, 7. Prime factorization of 45360 in exponential form is:

45360 = 24 × 34 × 51 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 45355 and 45360.

LCM(45355,45360) = 51 × 471 × 1931 × 24 × 34 × 71
LCM(45355,45360) = 411460560