What is the Least Common Multiple of 314 and 334?
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 314 and 334 is 52438.
LCM(314,334) = 52438
Least Common Multiple of 314 and 334 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 314 and 334, than apply into the LCM equation.
GCF(314,334) = 2
LCM(314,334) = ( 314 × 334) / 2
LCM(314,334) = 104876 / 2
LCM(314,334) = 52438
Least Common Multiple (LCM) of 314 and 334 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 314 and 334. First we will calculate the prime factors of 314 and 334.
Prime Factorization of 314
Prime factors of 314 are 2, 157. Prime factorization of 314 in exponential form is:
314 = 21 × 1571
Prime Factorization of 334
Prime factors of 334 are 2, 167. Prime factorization of 334 in exponential form is:
334 = 21 × 1671
Now multiplying the highest exponent prime factors to calculate the LCM of 314 and 334.
LCM(314,334) = 21 × 1571 × 1671
LCM(314,334) = 52438
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