What is the Least Common Multiple of 289 and 306?
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 306 is 5202.
LCM(289,306) = 5202
Least Common Multiple of 289 and 306 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 306, than apply into the LCM equation.
GCF(289,306) = 17
LCM(289,306) = ( 289 × 306) / 17
LCM(289,306) = 88434 / 17
LCM(289,306) = 5202
Least Common Multiple (LCM) of 289 and 306 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 289 and 306. First we will calculate the prime factors of 289 and 306.
Prime Factorization of 289
Prime factors of 289 are 17. Prime factorization of 289 in exponential form is:
289 = 172
Prime Factorization of 306
Prime factors of 306 are 2, 3, 17. Prime factorization of 306 in exponential form is:
306 = 21 × 32 × 171
Now multiplying the highest exponent prime factors to calculate the LCM of 289 and 306.
LCM(289,306) = 172 × 21 × 32
LCM(289,306) = 5202
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