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What is the Least Common Multiple of 254 and 260?

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 254 and 260 is 33020.

LCM(254,260) = 33020

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Least Common Multiple of 254 and 260 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 254 and 260, than apply into the LCM equation.

GCF(254,260) = 2
LCM(254,260) = ( 254 × 260) / 2
LCM(254,260) = 66040 / 2
LCM(254,260) = 33020

Least Common Multiple (LCM) of 254 and 260 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 254 and 260. First we will calculate the prime factors of 254 and 260.

Prime Factorization of 254

Prime factors of 254 are 2, 127. Prime factorization of 254 in exponential form is:

254 = 21 × 1271

Prime Factorization of 260

Prime factors of 260 are 2, 5, 13. Prime factorization of 260 in exponential form is:

260 = 22 × 51 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 254 and 260.

LCM(254,260) = 22 × 1271 × 51 × 131
LCM(254,260) = 33020