What is the Least Common Multiple of 392 and 399?
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 392 and 399 is 22344.
LCM(392,399) = 22344
Least Common Multiple of 392 and 399 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 392 and 399, than apply into the LCM equation.
GCF(392,399) = 7
LCM(392,399) = ( 392 × 399) / 7
LCM(392,399) = 156408 / 7
LCM(392,399) = 22344
Least Common Multiple (LCM) of 392 and 399 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 392 and 399. First we will calculate the prime factors of 392 and 399.
Prime Factorization of 392
Prime factors of 392 are 2, 7. Prime factorization of 392 in exponential form is:
392 = 23 × 72
Prime Factorization of 399
Prime factors of 399 are 3, 7, 19. Prime factorization of 399 in exponential form is:
399 = 31 × 71 × 191
Now multiplying the highest exponent prime factors to calculate the LCM of 392 and 399.
LCM(392,399) = 23 × 72 × 31 × 191
LCM(392,399) = 22344
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