What is the Least Common Multiple of 189 and 206?
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 189 and 206 is 38934.
LCM(189,206) = 38934
Least Common Multiple of 189 and 206 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 189 and 206, than apply into the LCM equation.
GCF(189,206) = 1
LCM(189,206) = ( 189 × 206) / 1
LCM(189,206) = 38934 / 1
LCM(189,206) = 38934
Least Common Multiple (LCM) of 189 and 206 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 189 and 206. First we will calculate the prime factors of 189 and 206.
Prime Factorization of 189
Prime factors of 189 are 3, 7. Prime factorization of 189 in exponential form is:
189 = 33 × 71
Prime Factorization of 206
Prime factors of 206 are 2, 103. Prime factorization of 206 in exponential form is:
206 = 21 × 1031
Now multiplying the highest exponent prime factors to calculate the LCM of 189 and 206.
LCM(189,206) = 33 × 71 × 21 × 1031
LCM(189,206) = 38934
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