What is the Least Common Multiple of 230 and 250?
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 230 and 250 is 5750.
LCM(230,250) = 5750
Least Common Multiple of 230 and 250 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 230 and 250, than apply into the LCM equation.
GCF(230,250) = 10
LCM(230,250) = ( 230 × 250) / 10
LCM(230,250) = 57500 / 10
LCM(230,250) = 5750
Least Common Multiple (LCM) of 230 and 250 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 230 and 250. First we will calculate the prime factors of 230 and 250.
Prime Factorization of 230
Prime factors of 230 are 2, 5, 23. Prime factorization of 230 in exponential form is:
230 = 21 × 51 × 231
Prime Factorization of 250
Prime factors of 250 are 2, 5. Prime factorization of 250 in exponential form is:
250 = 21 × 53
Now multiplying the highest exponent prime factors to calculate the LCM of 230 and 250.
LCM(230,250) = 21 × 53 × 231
LCM(230,250) = 5750
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