What is the Least Common Multiple of 364 and 380?
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 380 is 34580.
LCM(364,380) = 34580
Least Common Multiple of 364 and 380 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 380, than apply into the LCM equation.
GCF(364,380) = 4
LCM(364,380) = ( 364 × 380) / 4
LCM(364,380) = 138320 / 4
LCM(364,380) = 34580
Least Common Multiple (LCM) of 364 and 380 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 364 and 380. First we will calculate the prime factors of 364 and 380.
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 380
Prime factors of 380 are 2, 5, 19. Prime factorization of 380 in exponential form is:
380 = 22 × 51 × 191
Now multiplying the highest exponent prime factors to calculate the LCM of 364 and 380.
LCM(364,380) = 22 × 71 × 131 × 51 × 191
LCM(364,380) = 34580
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