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H.C.F and L.C.M interview questions and answers

16)
The L.C.M. of three different numbers is 120. Which of the following cannot be their H.C.F. ?
  • 8
  • 12
  • 24
  • 35
+ View Answer
  • Answer
  • d) 35
  • Solution
  • 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.

17)
The H.C.F. of two numbers is 8. Which one of the following can never be their L.C.M. ?
  • 24
  • 48
  • 56
  • 60
+ View Answer
  • Answer
  • d) 60
  • Solution
  • H.C.F. of two numbers divides their L.C.M. exactly.
    Clearly, 8 is not a factor of 60.

18)
The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is :
  • 276
  • 299
  • 322
  • 345
+ View Answer
  • Answer
  • c) 322
  • Solution
  • The numbers are (23 * 13) and (23 * 14)
    Larger number = (23 * 14) = 322.

19)
About the number of pairs which have 16 as their H.C.F. and 136 as their L.C.M., We can definitely say that :
  • no such pair exists
  • only one such pair exists
  • only two such pair exist
  • many such pair exist
+ View Answer
  • Answer
  • a) no such pair exists
  • Solution
  • Since 16 is not a factor of 136, it follows that there does not exist any pair of numbers with H.C.F. 16 and L.C.M. 136.

20)
The greatest number that exactly divides 105, 1001 and 2436 is :
  • 3
  • 7
  • 11
  • 21
+ View Answer
  • Answer
  • b) 7
  • Solution
  • H.C.F. of 2436 and 1001 is 7. Also, H.C.F. of 105 and 7 is 7.
    H.C.F. of 105, 1001 and 2436 is 7.