What is the Least Common Multiple of 189 and 198?
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 198 is 4158.
LCM(189,198) = 4158
Least Common Multiple of 189 and 198 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 198, than apply into the LCM equation.
GCF(189,198) = 9
LCM(189,198) = ( 189 × 198) / 9
LCM(189,198) = 37422 / 9
LCM(189,198) = 4158
Least Common Multiple (LCM) of 189 and 198 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 189 and 198. First we will calculate the prime factors of 189 and 198.
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 198
Prime factors of 198 are 2, 3, 11. Prime factorization of 198 in exponential form is:
198 = 21 × 32 × 111
Now multiplying the highest exponent prime factors to calculate the LCM of 189 and 198.
LCM(189,198) = 33 × 71 × 21 × 111
LCM(189,198) = 4158
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Related Least Common Multiples of 198
- LCM of 198 and 202
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