What is the Least Common Multiple of 188 and 205?
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 188 and 205 is 38540.
LCM(188,205) = 38540
Least Common Multiple of 188 and 205 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 188 and 205, than apply into the LCM equation.
GCF(188,205) = 1
LCM(188,205) = ( 188 × 205) / 1
LCM(188,205) = 38540 / 1
LCM(188,205) = 38540
Least Common Multiple (LCM) of 188 and 205 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 188 and 205. First we will calculate the prime factors of 188 and 205.
Prime Factorization of 188
Prime factors of 188 are 2, 47. Prime factorization of 188 in exponential form is:
188 = 22 × 471
Prime Factorization of 205
Prime factors of 205 are 5, 41. Prime factorization of 205 in exponential form is:
205 = 51 × 411
Now multiplying the highest exponent prime factors to calculate the LCM of 188 and 205.
LCM(188,205) = 22 × 471 × 51 × 411
LCM(188,205) = 38540
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