# Important Number System : HCF & LCM Notes For SSC CGL 2018

## Number System Concepts for SSC And Railway Exam:

Quantitative Aptitude is an equally important section for SSC CGL, CHSL, MTS exams and has an even more abundant importance in some other exams conducted by SSC. Generally, there are questions asked related to basic concepts and formulas of Number System.
To let you make the most of QUANT section, we are providing important facts related to Number System. Also, Railway Exam is nearby with bunches of posts for the interested candidates in which quantitative aptitude is a major part. We have covered important notes and questions focusing on these prestigious exams. We wish you all the best of luck to come over the fear of Mathematics section.

Number System

1. L.C.M. and H.C.F. of Fractions

L.C.M=(L.C.M.of the numbers in numerators)/(H.C.F.of in the number in denominator)
H.C.F=(H.C.F.of the numbers in numerators)/(L.C.M.of in the number in denominator)

2. Product of two numbers = L.C.M. of the numbers × H.C.F. of the numbers

3. To find the greatest number that will exactly divide x, y and z.

Required number = H.C.F. of x, y and z.

4. To find the greatest number that will divide x, y and z leaving remainders a, b and c, respectively.

Required number = H.C.F. of (x – a), (y – b) and (z – c).

5. To find the least number which is exactly divisible by x, y and z.

Required number = L.C.M. of x, y and z.

6. To find the least number which when divided by x, y and z leaves the remainders a, b and c, respectively. It is always observed that (x – a) = (y – b) = (z – c) = k (say)

∴ Required number = (L.C.M. of x, y and z) – k.

7. To find the least number which when divided by x, y and z leaves the same remainder r in each case.

Required number = (L.C.M. of x, y and z) + r

8. To find the greatest number that will divide x, y and z leaving the same remainder in each case.

(A) When the value of remainder r is given:
Required number = H.C.F. of (x – r), (y – r) and (z – r).
(B) When the value of the remainder is not given:
Required number = H.C.F. of |(x – y)|, |(y – z)| and |(z – x)|

9. To find the n-digit greatest number which, when divided by x, y and z.

(A) leaves no remainder (i.e., exactly divisible)

Step 1: L.C.M. of x, y and z = L
Step 2:
Step 3: Required number = n-digit greatest number — R

(B) leaves remainder K in each case.

Required number = (n-digit greatest number — R) + K.

10. To find the n-digit smallest number which when divided by x, y and z.

(A) leaves no remainder (i.e., exactly divisible)

Step 1: L.C.M. of x, y and z = L
Step 2:
Step 3: Required number = n-digit smallest number + (L – R).

(B) leaves remainder K in each case.

Required number = n-digit smallest number + (L – R) + k.