What is the Least Common Multiple of 364 and 384?
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 364 and 384 is 34944.
LCM(364,384) = 34944
Least Common Multiple of 364 and 384 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 364 and 384, than apply into the LCM equation.
GCF(364,384) = 4
LCM(364,384) = ( 364 × 384) / 4
LCM(364,384) = 139776 / 4
LCM(364,384) = 34944
Least Common Multiple (LCM) of 364 and 384 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 364 and 384. First we will calculate the prime factors of 364 and 384.
Prime Factorization of 364
Prime factors of 364 are 2, 7, 13. Prime factorization of 364 in exponential form is:
364 = 22 × 71 × 131
Prime Factorization of 384
Prime factors of 384 are 2, 3. Prime factorization of 384 in exponential form is:
384 = 27 × 31
Now multiplying the highest exponent prime factors to calculate the LCM of 364 and 384.
LCM(364,384) = 27 × 71 × 131 × 31
LCM(364,384) = 34944
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