What is the Least Common Multiple of 188 and 204?
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 204 is 9588.
LCM(188,204) = 9588
Least Common Multiple of 188 and 204 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 204, than apply into the LCM equation.
GCF(188,204) = 4
LCM(188,204) = ( 188 × 204) / 4
LCM(188,204) = 38352 / 4
LCM(188,204) = 9588
Least Common Multiple (LCM) of 188 and 204 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 188 and 204. First we will calculate the prime factors of 188 and 204.
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 204
Prime factors of 204 are 2, 3, 17. Prime factorization of 204 in exponential form is:
204 = 22 × 31 × 171
Now multiplying the highest exponent prime factors to calculate the LCM of 188 and 204.
LCM(188,204) = 22 × 471 × 31 × 171
LCM(188,204) = 9588
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