What is the Least Common Multiple of 230 and 249?
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 249 is 57270.
LCM(230,249) = 57270
Least Common Multiple of 230 and 249 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 249, than apply into the LCM equation.
GCF(230,249) = 1
LCM(230,249) = ( 230 × 249) / 1
LCM(230,249) = 57270 / 1
LCM(230,249) = 57270
Least Common Multiple (LCM) of 230 and 249 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 230 and 249. First we will calculate the prime factors of 230 and 249.
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 249
Prime factors of 249 are 3, 83. Prime factorization of 249 in exponential form is:
249 = 31 × 831
Now multiplying the highest exponent prime factors to calculate the LCM of 230 and 249.
LCM(230,249) = 21 × 51 × 231 × 31 × 831
LCM(230,249) = 57270
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