What is the Least Common Multiple of 289 and 305?
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 289 and 305 is 88145.
LCM(289,305) = 88145
Least Common Multiple of 289 and 305 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 289 and 305, than apply into the LCM equation.
GCF(289,305) = 1
LCM(289,305) = ( 289 × 305) / 1
LCM(289,305) = 88145 / 1
LCM(289,305) = 88145
Least Common Multiple (LCM) of 289 and 305 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 289 and 305. First we will calculate the prime factors of 289 and 305.
Prime Factorization of 289
Prime factors of 289 are 17. Prime factorization of 289 in exponential form is:
289 = 172
Prime Factorization of 305
Prime factors of 305 are 5, 61. Prime factorization of 305 in exponential form is:
305 = 51 × 611
Now multiplying the highest exponent prime factors to calculate the LCM of 289 and 305.
LCM(289,305) = 172 × 51 × 611
LCM(289,305) = 88145
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