# LCM & HCF

Pratice LCM & HCF Questions and answers.

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.