What is the Least Common Multiple of 250 and 255?
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 250 and 255 is 12750.
LCM(250,255) = 12750
Least Common Multiple of 250 and 255 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 250 and 255, than apply into the LCM equation.
GCF(250,255) = 5
LCM(250,255) = ( 250 × 255) / 5
LCM(250,255) = 63750 / 5
LCM(250,255) = 12750
Least Common Multiple (LCM) of 250 and 255 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 250 and 255. First we will calculate the prime factors of 250 and 255.
Prime Factorization of 250
Prime factors of 250 are 2, 5. Prime factorization of 250 in exponential form is:
250 = 21 × 53
Prime Factorization of 255
Prime factors of 255 are 3, 5, 17. Prime factorization of 255 in exponential form is:
255 = 31 × 51 × 171
Now multiplying the highest exponent prime factors to calculate the LCM of 250 and 255.
LCM(250,255) = 21 × 53 × 31 × 171
LCM(250,255) = 12750
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