NUMBERS – Important Notes/Formulae

(1) If a number “N” when divided by a,b,c leaves the same remainder ‘r’, then
“N” can be expressed in the below formats
N = LCM(a,b,c) + r
and
N = HCF [ (c-a), (c-b) ]

(2) If “N” is divides a,b,c and leaves same remainder, then
N=k(a-b) (k can take fractional values as well)

(3) If a number “N” when divided by a,b,c leaves the remainders (a-x), (b-y), (c-z), then
N = LCM(a,b,c) – x

(4) LCM and HCF of Fractions
LCM [ (a/x), (b/y), (c/z) ] = LCM (a,b,c) / HCF (x,y,z)
HCF [ (a/x), (b/y), (c/z) ] = HCF (a,b,c) / LCM (x,y,z)

(5) a*b = LCM(a,b) * HCF(a,b)