| Rule | Description |
|---|---|
| 1 | \[1st\ number\times2nd\ number=L.C.M.\times H.C.F.\] |
| 2 | \[L.C.M.\ of\ fractions\ =\ \frac{L.C.M.\ of\ numerators}{H.C.F.\ of\ denominators}\] |
| 3 | \[H.C.F.\ of\ fractions\ =\ \frac{H.C.F.\ of\ numerators}{L.C.F.\ of\ denominators}\] |
| 4 |
When a number is divided by a, b or c leaving same remainder ‘r’ in each case then that number must be \[k + r\] where k is LCM of a, b and c. |
| 5 |
When a number is divided by a, b or c leaving remainders p, q or r respectively such that the difference between divisor and remainder in each case is same i.e., \[(a – P) = (b – q) = (c – r) = t\] then that (least) number must be in the form of \[(k – t)\], where k is LCM of a, b and c. |
| 6 |
The largest number which when divide the numbers a, b and c the remainders are same then that largest number is given by H.C.F. of \[(a – b), (b – c), (c – a)\]. |
| 7 |
The largest number which when divide thenumbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of \[(a – p), (b – q), (c – r)\]. |
| 8 |
Greatest n digit number which when divided by three numbers p, q, r leaves no remainder will be Required Number \[= (n \ – \ \text{digit greatest number}) \ - R\] R is the remainder obtained on dividing greatest n digit number by L.C.M of p, q, r. |
| 9 |
The n digit largest number which when dividedby p, q, r leaves remainder ‘a’ will be Required number \[= [n \ – \text{digit largest number} \ – \ R] + a\] where, R is the remainder obtained when \[n \ – \ \text{digit largest number}\] is divided by the L.C.M of p, q, r. |