What is the Least Common Multiple of 225 and 238?
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 225 and 238 is 53550.
LCM(225,238) = 53550
Least Common Multiple of 225 and 238 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 225 and 238, than apply into the LCM equation.
GCF(225,238) = 1
LCM(225,238) = ( 225 × 238) / 1
LCM(225,238) = 53550 / 1
LCM(225,238) = 53550
Least Common Multiple (LCM) of 225 and 238 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 225 and 238. First we will calculate the prime factors of 225 and 238.
Prime Factorization of 225
Prime factors of 225 are 3, 5. Prime factorization of 225 in exponential form is:
225 = 32 × 52
Prime Factorization of 238
Prime factors of 238 are 2, 7, 17. Prime factorization of 238 in exponential form is:
238 = 21 × 71 × 171
Now multiplying the highest exponent prime factors to calculate the LCM of 225 and 238.
LCM(225,238) = 32 × 52 × 21 × 71 × 171
LCM(225,238) = 53550
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