**Q1.**12

^{2},12

^{4},12

^{10},12

^{6}Find the L.C.M.

^{2}c)12

^{6}d)12

^{10}

^{}

**Q2.**6

^{-1},6

^{-3},6

^{-10},6

^{-12}Find the H.C.F.

a) 6

^{-1}b) 1 c)6

^{-12}d)6

^{-11}

**Q3.**The L.C.M of the fraction of

^{2}/3,

^{4}/9,

^{5}/6,

^{7}/12 is:

^{35}/9 b)

^{1}/36 c)

^{1}/18 d)

^{140}/3

**Q4.**

**The ratio of two number is 5:6, if their H,C.F. is 9 and L.C.M. is 270. Find the numbers.**

a) 72,63 b) 81,108 c) 45,54 d) 225,108

**Q5.**The multiplication of two numbers is 20,000 if their L.C.M is 800. Find the H.C.F.

a)400 b) 25 c) 2,000 d) 800

**Q6.**Find the least number which when divided by 4,6,7,8,9,12. leaves the same remainder 3 in each case.

a) 504 b) 501 c) 507 d) 506

**Q7.**The smallest number which is divisible by 12,15,20 and is a perfect square is:

a) 400 b) 900 c) 1600 d) 3600

**Q8.**The largest number which divided by 77, 147 and 252 to leave the same remainder in each case is:

a) 9 b) 15 c)35 d) 25

**Q9.**The H.C.F. of the fraction of

^{36}/25,

^{48}/25,

^{72}/75

a)

^{12}/75 b)

^{4}/25 c)

^{36}/25 d)

^{36}

###
**
Solution:**

Sol: Option (d)

**(1)**Sol: Option (d)

^{2},12

^{4},12

^{10},12

^{6}Find the L.C.M.

L.C.M. = 12

^{10}

**(2)**

**Sol:**Option(c)

^{-1},6

^{-3},6

^{-10},6

^{-12}Find the H.C.F.

^{1}/_{6},^{1}/_{63 },^{1}/_{610 },^{1}/_{612 }^{H.C.F.}/

_{L.C.M.}=

^{1}/

_{612 }

= 16

^{-12}

**(3)**

**Sol: Option (d)**

^{L.C.M.}/H.C.F. =

^{140}/3

**(4)**

**Sol:**

**Option (c)**

The ratio of numbers is 5:6

The number is 5✘9=45

=6✘9=54

**(5)**

**Sol: Option (b)**

L.C.M.✘H.C.F. = Ist No✘2nd No.

800✘H.C.F. = 20,000

H.C.F. =

^{20,000}/

_{800}= 25

**(6)**

**Sol: Option (c)**

L.C.M. of the number 4,6,7,8,9,12

L.C.M. = 8✘9✘7 = 504

and Remainder = 3

So the number is L.C.M. + 3

504 + 3 = 507

**(7)**

**Sol:**

**Option (b)**

L.C.M. = (3✘5✘2

^{2})

Required number = ( 3

^{2}✘5

^{2}✘2

^{2})=900

**(8)**

**Sol:**

**Option (c)**

Required number = H.C.F. of (147-77)

(252-147) and (252-77)

= H.C.F. of 70,105 and 175

= 35

( 70 = 2✘5✘7, 105 = 5✘3✘7 and 175=5✘5✘7 )

H.C.F. =5✘7 = 35

**(9)**

**Sol:**

**Option (a)**

=

^{H.C.F. of numerator}/ L.C.M. of denominator

H.C.F.=

^{12}/75

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