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What is the Least Common Multiple of 45264 and 45270?

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 45264 and 45270 is 341516880.

LCM(45264,45270) = 341516880

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Least Common Multiple of 45264 and 45270 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45264 and 45270, than apply into the LCM equation.

GCF(45264,45270) = 6
LCM(45264,45270) = ( 45264 × 45270) / 6
LCM(45264,45270) = 2049101280 / 6
LCM(45264,45270) = 341516880

Least Common Multiple (LCM) of 45264 and 45270 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45264 and 45270. First we will calculate the prime factors of 45264 and 45270.

Prime Factorization of 45264

Prime factors of 45264 are 2, 3, 23, 41. Prime factorization of 45264 in exponential form is:

45264 = 24 × 31 × 231 × 411

Prime Factorization of 45270

Prime factors of 45270 are 2, 3, 5, 503. Prime factorization of 45270 in exponential form is:

45270 = 21 × 32 × 51 × 5031

Now multiplying the highest exponent prime factors to calculate the LCM of 45264 and 45270.

LCM(45264,45270) = 24 × 32 × 231 × 411 × 51 × 5031
LCM(45264,45270) = 341516880