## Number System Concepts for SSC And Railway Exam:

**we are providing important facts related to Number System**.

**We wish you all the best of luck to come over the fear of Mathematics section.**

*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.*__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.

**Required number = H.C.F. of (x – r), (y – r) and (z – r).**

**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 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 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.**