LCM and HCF
1. The LCM of two numbers
is 864 and their HCF is 144. If one of the number is 288, the other number is
(1) 576
(2) 1296 (3) 432 (4) 144 (5) None of these
2. The HCF of two numbers
is 12906 and 14818 is 478. Their LCM is
(1) 400086
(2) 200043 (3) 600129 (4) 800172 (5) None of these
3. The HCF and LCM of two
2 digit numbers are 16 and 480 respectively. The numbers are
(1) 40, 48
(2) 60, 72
(3) 64,
80 (4) 80, 96 (5) None of these
4. The product of two
numbers is 4107. If the HCF of the numbers is 37. The greater number is
(1) 185 (2) 111 (3) 107 (4) 101 (5) None of these
5. The HCF and LCM of two
numbers are 12 and 924 respectively. Then the number of such pair is
(1) 0 (2) 1 (3) 2 (4) 3 (5) None of these
6. The HCF and product of
two numbers are 15 and 6300 respectively. The number of possible pairs of the
numbers is
(1) 4 (2) 3 (3) 2 (4) 1 (5) None of these
7. Product of two
co-prime numbers is 117. Then their LCM is
(1) 117 (2) 9 (3) 13 (4) 39 (5) None of these
8. The HCF and LCM of two
numbers are 13 and 455 respectively. If one of the numbers lies between 75 and
125, then that number is
(1) 78 (2) 91 (3) 104 (4) 117 (5) None of these
9. The HCF of two numbers
is 8, Which one of the following can never be their LCM
(1) 24 (2) 48 (3) 56 (4) 60 (5) None of these
10. The HCF of two numbers
is 23 and the other two factors of their LCM are 13 and 14. The larger of the
two numbers is
(1) 276 (2) 299 (3) 345 (4) 322 (5) None of these
11. The LCM of three
different numbers is 120. Which of the following cannot be their HCF
(1) 8 (2) 12 (3) 24 (4) 35 (5) None of these
12. The HCF and LCM of two
numbers are 44 and 264 respectively. If the first number is divided by 2, the
quotient is 44.The other number is
(1) 147 (2) 528 (3) 132 (4) 264 (5) None
of these
13. The least number which
when divided by 4, 6, 8, 12 and 16 leaves a remainder of 2 in each case
(1) 46 (2) 48 (3) 50 (4) 56 (5) None of these
14. Find the greatest
number of five digits which when divided by 3, 5, 8, 12 have 2 as remainder
(1) 99999 (2) 99958 (3) 99960 (4) 99962 (5) None
of these
15. The least perfect
square, which is divisible by each 21, 36 and 66 is
(1) 214344
(2) 214434 (3) 213444 (4) 231444 (5) None of these
16. If the students of a
class can be grouped exactly into 6 or 8 or 10, then the minimum number of
students in the class must be
(1) 60 (2) 120 (3) 180 (4) 240 (5) None of these
17. The least number which
when divided by 4, 6, 8 and 9 leave zero remainder in each case and when
divided by 13 leaves a remainder of 7 is
(1) 144 (2) 72 (3) 36 (4) 85 (5) None of these
18. A number which when
divided by 10 leaves remainder 9, when divided by 9 leaves remainder of 8 and
when divided by 8 leaves remainder of 7 is
(1) 1539 (2) 539 (3) 359 (4) 1359 (5) None of these
19. The traffic lights at
three different road crossings change after 24 seconds, 36 seconds and 54
seconds respectively. If they all change simultaneously at 10 : 15 : 00 AM,
then at what time will they again change simultaneously ?
(1) 10 : 16 : 54 AM
(2) 10 : 18 : 36 AM
(3) 10 : 17 : 02 AM
(4) 10 : 22 : 12 AM
(5) None of these
20. 4 bells ring at
intervals of 30 min, 1 hr, 1
hr and 1 hr 45
min respectively. All the bells ring simultaneously at 12 noon. They will again
ring simultaneously at
hr and 1 hr 45
min respectively. All the bells ring simultaneously at 12 noon. They will again
ring simultaneously at
(1) 12 mid night
(2) 3 AM (3) 6 AM (4) 9 AM (5) None of these
21. The number nearest to
10000, which is exactly divisible by each of 3, 4, 5, 6, 7 and 8 is
(1) 9240 (2) 10080 (3) 9996 (4) 10000 (5) None of these
22. Three men step off
together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm
respectively. The minimum distance each should cover so that all can cover the
distance in complete steps is
(1) 6930 cm
(2) 9360 cm (3) 6930 cm (4) 6950 cm (5) None of these
23. The maximum number of
students among whom 1001 pens and 910 pencils can be distributed in such a way
that each student gets same number of pens and same number of pencils is
(1) 91
(2) 910 (3) 1001 (4) 1911 (5) None of these
24. Let N be the greatest
number that will divide 1305, 4665 and 6905 leaving the same remainder in each
case. Then , sum of the digits in N is
(1) 4
(2) 5 (3) 6 (4) 8 (5) None of these
25. What is the least
number of square tiles required to pave the floor of a room 15 m 17 cm long and
9 m 2 cm broad?
(1) 840 (2) 841 (3) 820 (4) 814 (5) None of these
26. Three sets of English,
Mathematics and Science books containing 336, 240, 96 books respectively have
to be stacked in such a way that all the books are stored subject –wise and the
height of each stack is the same. Total number of stacks will be
(1) 14 (2) 21 (3) 22 (4) 48 (5) None of these
27. The LCM and the HCF of
the numbers 28 and 42 are in the ratio
(1) 6 : 1 (2) 2 : 3 (3)
3 : 2 (4) 7 : 2 (5) None
of these
28. The ratio of the sum
to the LCM of two natural numbers is 7 : 12. If their HCF is 4, then the smaller
number is
(1) 20 (2) 16 (3)
12 (4) 8 (5)
None of these
29. Two numbers are in the
ratio 3 : 4. The product of their HCF and LCM is 2028. The sum of the numbers
is
(1) 68 (2) 72 (3)
86 (4) 91 (5)
None of these
30. The product of the LCM
and HCF of two numbers is 24. The difference of the two numbers is 2. Find the
numbers
(1) 8 and 6
(2) 8 and 10 (3) 2 and
4 (4) 6 and 4 (5)
None of these
31. The LCM of two numbers
is 495 and their HCF is 5. If the sum of the numbers is 100.Then their
difference is
(1) 10 (2) 46 (3) 70 (4) 70 (5)
None of these
32. The LCM of two
multiplies of 12 is 1056. If one of the number is 132, the other number is
(1) 12 (2) 72 (3) 96 (4) 132 (5) None of these
33. If P = 23.310.5
; Q = 25.3.7, then HCF of P and Q is
(1) 2.3.5.7
(2) 3.23
(3) 22.37 (4) 25.310.5.7 (5) None of these
34. The number of pair of
positive integers whose sum is 99 and HCF is 9 is
(1) 2 (2) 4 (3) 4 (4) 5 (5) None of these
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