What is the Least Common Multiple of 12189 and 12199?
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 12189 and 12199 is 148693611.
LCM(12189,12199) = 148693611
Least Common Multiple of 12189 and 12199 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12189 and 12199, than apply into the LCM equation.
GCF(12189,12199) = 1
LCM(12189,12199) = ( 12189 × 12199) / 1
LCM(12189,12199) = 148693611 / 1
LCM(12189,12199) = 148693611
Least Common Multiple (LCM) of 12189 and 12199 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 12189 and 12199. First we will calculate the prime factors of 12189 and 12199.
Prime Factorization of 12189
Prime factors of 12189 are 3, 17, 239. Prime factorization of 12189 in exponential form is:
12189 = 31 × 171 × 2391
Prime Factorization of 12199
Prime factors of 12199 are 11, 1109. Prime factorization of 12199 in exponential form is:
12199 = 111 × 11091
Now multiplying the highest exponent prime factors to calculate the LCM of 12189 and 12199.
LCM(12189,12199) = 31 × 171 × 2391 × 111 × 11091
LCM(12189,12199) = 148693611
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