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1. H.C.F AND L.C.M
Questions and Answers

2. 1) 504 can be expressed as a product of primes as ?
1)2 ×2 × 2 × 3 × 3 × 7
1)2 ×3 × 2 × 3 × 3 × 7
1)3 ×2 × 2 × 3 × 3 × 7
2)None of these
Explanation :- 504 can be expressed as 2 ×2 × 2 × 3 × 3 × 7.
Ans :- 2 ×2 × 2 × 3 × 3 × 7

3. 2) Calculate the L.C.M. of 148 and 185 ?
1)720
2)540
3)820
4)740
Explanation :- H.C.F. of 148 and 185 is 37.
∴ L.C.M. = [ (148 × 185) / 37 ] = 740 .
Ans :- 740

4. 3) Find the highest length which can be used to measure exactly the
lengths 7m, 6m 45 cm, 12m 95 cm ?
1) 38 cm
2) 34 cm
3) 35 cm
4) 30 cm
Explanation :- First we have to convert metre into cms
Required length = H.C.F. of 700cm , 645 cm and 1295 cm =
35cm.
Ans :- 35 cm

5. 4) Find the L.C.M of 12,16,20,24
1)290
2)340
3)480
4)238
Explanation :- The above numbers will become 3,4,5,6
when they divided by 4
Again 3,4,5,6 can be formed as 1,4,5,2 when divided by 3
So, 4 × 3 × 1 × 4 × 5 × 2 = 480.
Ans :- 480

6. 5) Find the L.C.M. of 2/3 , 3/5 , 4/7 , 9/13 ?
1)12
2)34
3)45
4) 36
Explanation :- L.C.M. = [ (L.C.M. of 2, 3, 4, 9 ) / (H.C.F.
of 3, 5, 7, 13) ] = 36/1 = 36.
Ans :- 36

7. 6) Find the least number which when divided by 28,40,52 and 130
leaves 18,30,42 and 120 as reminders respectively?
1) 3630
2) 3730
3) 3620
4) 2630
Explanation :- Here (28 - 18) = 10, (40 - 30) = 10, (52 - 42) = 10,
(130 - 120) = 10
∴ Required number = (L.C.M. of 28, 40, 52, 130) – 10 = 3640 –
10 = 3630 .
Ans :- 3630

8. 7) Find the other number when the two numbers H.C.F and L.C.M
are 11 and 7700 respectively, where the first number is 275?
1) 301
2) 308
3) 312
4) 378
Explanation :- Other number = [ (11 × 7700) / 275 ] = 308.
Ans :- 312

9. 8) Find the smallest fraction, with which each of 6/7 , 5/14 , 10/21 will
divide exactly?
1) 30 / 8
2) 30 / 9
3) 30 / 7
4) 30 /1
Explanation :- Needed answer = L.C.M. of 6/7 , 5/14 , 10/21 = [
(L.C.M. of 6, 5, 10) / (H.C.F. of 7, 14, 21) ] = 30/7 .
Ans :- 30 / 7

10. 9) If the L.C.M. of three numbers is 120. Which of the following
cannot be their H.C.F ?
1) 16
2) 73
3) 92
4) 35
Explanation :- Since H.C.F. is always a factor of L.C.M., we cannot
have three numbers with H.C.F. 35 and L.C.M. 120.
Ans :- 35

11. 10) If the product of two numbers is 1880 and their H.C.F. is 5. Then
find the L.C.M. of the numbers ?
1) 389
2) 346
3) 378
4) 376
Explanation :- L.C.M. = [ (product of numbers) / (H.C.F.) ] =
1880 / 5 = 376.
Ans :- 376

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