What is the Least Common Multiple of 385 and 400?
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 385 and 400 is 30800.
LCM(385,400) = 30800
Least Common Multiple of 385 and 400 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 385 and 400, than apply into the LCM equation.
GCF(385,400) = 5
LCM(385,400) = ( 385 × 400) / 5
LCM(385,400) = 154000 / 5
LCM(385,400) = 30800
Least Common Multiple (LCM) of 385 and 400 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 385 and 400. First we will calculate the prime factors of 385 and 400.
Prime Factorization of 385
Prime factors of 385 are 5, 7, 11. Prime factorization of 385 in exponential form is:
385 = 51 × 71 × 111
Prime Factorization of 400
Prime factors of 400 are 2, 5. Prime factorization of 400 in exponential form is:
400 = 24 × 52
Now multiplying the highest exponent prime factors to calculate the LCM of 385 and 400.
LCM(385,400) = 52 × 71 × 111 × 24
LCM(385,400) = 30800
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