Arithmatical - HCF and LCM of Numbers

DIRECTIONS : Problems based on HCF and LCM.
11. The maximum numbers of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is
  A.  91
  B.  910
  C.  1001
  D.  1911
Solution
Required number of students.
= H.C.F of 1001 and 910.
‹=› 91.
12. 252 can be expressed as a product of prime as
  A.  2 x 2 x 3 x 3 x 7
  B.  2 x 2 x 2 x 3 x 7
  C.  3 x 3 x 3 x 3 x 7
  D.  2 x 3 x 3 x 3 x 7
Solution
Clearly, 252 =2 x 2 x 3 x 3 x 7
13. Three different containers contain 496 litres, 403 litres and 713 litres of mixtures of milk and water respectively. What biggest measure can measure all the different quantities exactly?
  A.  1 litre
  B.  7 litre
  C.  31 litre
  D.  41 litre
Solution
Required measurement= H.C.F of (496, 403, 713) litres
‹=›31 litres.
14. The H.C.F of two numbers is 8. Which one of the following can never be their L.C.M?
  A.  8
  B.  12
  C.  60
  D.  72
Solution
H.C.F of two numbers divides their L.C.M exactly.
Clearly, 8 is not a factor of 60.
15. The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 10, then their difference is
  A.  10
  B.  46
  C.  70
  D.  90
Solution
Let the numbers be x and (100 - x) .
Then, x (100 - x) = 5 ×495
‹=›x2 - 100x + 2475 = 0.
‹=› (x -55) (x - 45) = 0.
x = 55 or x = 45.
Therefore, the numbers are 45 and 55.
Required difference = (55 - 45) = 10.
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