What is the Least Common Multiple of 294 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 294 and 306 is 14994.
LCM(294,306) = 14994
Least Common Multiple of 294 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 294 and 306, than apply into the LCM equation.
GCF(294,306) = 6
LCM(294,306) = ( 294 × 306) / 6
LCM(294,306) = 89964 / 6
LCM(294,306) = 14994
Least Common Multiple (LCM) of 294 and 306 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 294 and 306. First we will calculate the prime factors of 294 and 306.
Prime Factorization of 294
Prime factors of 294 are 2, 3, 7. Prime factorization of 294 in exponential form is:
294 = 21 × 31 × 72
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 294 and 306.
LCM(294,306) = 21 × 32 × 72 × 171
LCM(294,306) = 14994
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