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What is the Least Common Multiple of 10280 and 10300?

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 10280 and 10300 is 5294200.

LCM(10280,10300) = 5294200

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Least Common Multiple of 10280 and 10300 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10280 and 10300, than apply into the LCM equation.

GCF(10280,10300) = 20
LCM(10280,10300) = ( 10280 × 10300) / 20
LCM(10280,10300) = 105884000 / 20
LCM(10280,10300) = 5294200

Least Common Multiple (LCM) of 10280 and 10300 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10280 and 10300. First we will calculate the prime factors of 10280 and 10300.

Prime Factorization of 10280

Prime factors of 10280 are 2, 5, 257. Prime factorization of 10280 in exponential form is:

10280 = 23 × 51 × 2571

Prime Factorization of 10300

Prime factors of 10300 are 2, 5, 103. Prime factorization of 10300 in exponential form is:

10300 = 22 × 52 × 1031

Now multiplying the highest exponent prime factors to calculate the LCM of 10280 and 10300.

LCM(10280,10300) = 23 × 52 × 2571 × 1031
LCM(10280,10300) = 5294200