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What is the Least Common Multiple of 26500 and 26510?

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 26500 and 26510 is 70251500.

LCM(26500,26510) = 70251500

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Least Common Multiple of 26500 and 26510 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 26500 and 26510, than apply into the LCM equation.

GCF(26500,26510) = 10
LCM(26500,26510) = ( 26500 × 26510) / 10
LCM(26500,26510) = 702515000 / 10
LCM(26500,26510) = 70251500

Least Common Multiple (LCM) of 26500 and 26510 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 26500 and 26510. First we will calculate the prime factors of 26500 and 26510.

Prime Factorization of 26500

Prime factors of 26500 are 2, 5, 53. Prime factorization of 26500 in exponential form is:

26500 = 22 × 53 × 531

Prime Factorization of 26510

Prime factors of 26510 are 2, 5, 11, 241. Prime factorization of 26510 in exponential form is:

26510 = 21 × 51 × 111 × 2411

Now multiplying the highest exponent prime factors to calculate the LCM of 26500 and 26510.

LCM(26500,26510) = 22 × 53 × 531 × 111 × 2411
LCM(26500,26510) = 70251500