LCM and HCF
Q1. LCM of , ,
is
(a)
(b)
(c)
(d)
Q2. HCF of
, , and is
(a)
(b)
(c)
(d)
Q3. The LCM of two numbers is 864 and their
HCF is 144. If one number is 288, the other
number is:
(a) 576
(c) 432
(b) 299
(d) 322
Q5. 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:
(a) 144
(c) 36
(b) 72
(d) 85
Q6. The LCM and the HCF of the numbers 28
and 42 are in the ratio:
(a) 6:1
(c) 3:2
(b) 2:3
(d) 7:2
Q7. Three numbers are in the ratio 2:3:4 and
their HCF is 12. The LCM of the number is
(a) 144
(c) 96
(a) 14
(c) 22
(b) 21
(d) 48
Q9. The greatest number that will divide 729
and 901 leaving remainders 9 and 5
respectively, is
(a) 15
(c) 19
(b) 16
(d) 20
(b) 1296
(d) 144
Q4. The HCF of two numbers is 23 and the
other two factors of their LCM are 13 and 14.
The larger number is(a) 276
(c) 345
Q8. 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
numbers if stacks will be
(b) 192
(d) 72
Q10. 4 bells ring at intervals of 30 minutes, 1
hour, 1 hour and 1 hour 45 minutes
respectively. All the bells ring simultaneously
at 12 noon. They will again ring simultaneously
at
(a) 12 mid night
(c) 6 a.m.
(b) 3 a.m.
(d) 9 a.m.
Q11.The HCF (GCF) of a, b is 12, a, b are
positive integers and a> b>12.The smallest
values of (a, b) are respectively
(a) 12, 24
(c) 24, 36
(b) 24, 12
(d) 36, 24
Q12. Two numbers are in the ratio 3:4. The
product of their HCF and LCM is 2028. The sum
of the numbers is
(a) 68
(c) 86
(b) 72
(d) 91
Q13. The sum of two numbers is 36 and their
HCF is 4. How many pairs of such numbers are
possible?
(a) 1
(b) 2
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LCM and HCF
(c) 3
(d) 4
Q14. The LCM of two numbers is 12 times their
HCF. The sum of the HCF and LCM is 403. If one
of the number is 93, then the other number is
(a) 124
(c) 134
(b) 128
(d) 138
Q15. The greatest number, which when
subtracted from 5834, gives a number exactly
divisible by each of 20, 28, 32 and 35, is by
(a) 1120
(c) 5200
(b) 4714
(d) 5600
Q16. Six bells commence tolling together and
toll at intervals of 2, 4, 6, 8 10 and 12 seconds
respectively. In 30 minutes, how many times
do they toll together ?
(a) 4
(c) 15
(b) 10
(d) 16
(a) 28
(c) 40
(b) 32
(d) 64
Q21. If the sum of two numbers is 55 and the
H.C.F. and L.C.M. of these numbers are 5 and
120 respectively, then the sum of the
reciprocals of the numbers is equal to:
(a) 55/601
(c) 11/120
(b) 601/55
(d) 120/11
Q22. A, B and C start at the same time in the
same direction to run around a circular
stadium. A completes a round in 252 seconds,
B in 308 seconds and c in 198 seconds, all
starting at the same point. After what time will
they again at the starting point ?
(a) 26 min and 18 sec
(c) 45 min
(b) 42 min and 36 sec
(d) 46 min and 12 sec
Q17. The product of two numbers is 4107. If
the H.C.F. of these numbers is 37, then the
greater number is:
Q23. The traffic lights at three different road
crossings change after every 48 sec., 72 sec and
108 sec. respectively .If they all change
simultaneously at 8:20:00 hours, then at what
time they again change simultaneously
(a) 101
(c) 111
(a) 7 min and 18 sec
(c) 18 min and 10 sec
(b) 107
(d) 185
(b) 10 min and 18 sec
(d) 6 min and 28 sec
Q18. The H.C.F. of two numbers is 11 and their
L.C.M. is 7700. If one of the numbers is 275,
then the other is:
Q24. Find the greatest possible length which
can be used to measure exactly the lengths 4
m 95 cm, 9 m and 16 m 65 cm.
(a) 279
(c) 308
(a) 50 cm
(c) 55 cm
(b) 283
(d) 318
Q19. The least number, which when divided by
12, 15, 20 and 54 leaves in each case a
remainder of 8 is:
(a) 504
(c) 544
(b) 536
(d) 548
Q20. The L.C.M. of two numbers is 48. The
numbers are in the ratio 2 : 3. Then sum of the
number is:
(b) 45 cm
(d) 60 cm
Q25. Find the H.C.F. of 23 X 32 X 5 X 74, 22 X
35 X 52 X 73, 23 X 53 X 72
(a) 1000
(c) 800
(b) 980
(d) 900
Q26. Find the least number which when
divided by 6,7,8,9, and 12 leave the same
remainder 1 each case
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LCM and HCF
(a) 500
(c) 550
(b) 505
(d) 490
Q27. Find the least number which when
divided by 20,25,35 and 40 leaves remainders
14,19,29 and 34 respectively.
(a) 1400
(c) 1406
(b) 1394
(d) 1200
Q28. Find the least number which when
divided by 5,6,7, and 8 leaves a remainder 3,
but when divided by 9 leaves no remainder.
(a) 1683
(c) 2520
(b) 843
(d) 1600
Q29. A man was employed on the promise that
he will be paid the highest wages per day. The
contract money to be paid was Rs. 1189.
Finally he was paid only Rs. 1073. For how
many days did he actually work?
(a) 39
(c) 37
(b) 40
(d) 35
Q30. An officer was appointed on maximum
daily wages on contract money of Rs. 4956. But
on being absent for some days, he was paid
only Rs. 3894. For how many days was he
absent?
(a) 3
(c) 5
(b) 4
(d) 6
Q31. A wholesale tea dealer 408 kilograms,
468 kilograms and 516 kilograms of three
different qualities of tea. He wants it all to be
packed into boxes of equal size without
mixing. Find the capacity of the largest
possible box?
(a) 50
(c) 24
(b) 36
(d) 12
Q32. Find the least number which when
divided by 35 leaves remainder 25, when
divided by 25 leaves remainder 15 and when
divided by 15 leaves remainder 5?
(a) 420
(c) 435
(b) 515
(d) 518
Q33. Three men start together to travel the
same way around a circular track of 11
kilometers in circumference. Their speeds are
4, 5 and 8 kilometers per hour respectively.
When will they meet at a starting point?
(a) 11 hours
(c) 220 hours
(b) 12 hours
(c) 22 hours
Q34. The H.C.F and L.C.M of two numbers are
84 and 21 respectively. If the ratio of the two
numbers is 1:4, then the larger of the two
numbers is:
(a) 12
(c) 84
(b) 48
(d) 108
Q35. Three numbers which are co-prime to
each other are such that the product of the
first two is 551 and that of the last two is 1073.
The sum of the three numbers is :
(a) 75
(c) 85
(b) 81
(d) 98
Q36. A room is 6 meters 24 centimeters in
length and 4 meters 32 centimeters in width.
Find the least number of square tiles of equal
size required to cover the entire floor of the
room?
(a) 110
(c) 96
(b) 124
(d) 117
Q37. A drink vendor has 80 liters of Maaza, 144
liters of Pepsi and 368 liters of Sprite. He wants
to pack them in cans, so that each can contains
the same number of liters of a drink, and
doesn't want to mix any two drinks in a can.
What is the least number of cans required?
(a) 35
(b) 37
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LCM and HCF
(c) 42
(d) 30
Q38. The sum of two numbers is 36 and their
HCF is 4. How many pairs of such numbers are
possible ?
(a) 1
(c) 3
Q45. Which greatest possible length can be
used to measure exactly 15 meter 75 cm, 11
meter 25 cm and 7 meter 65 cm
(a) 45 cm
(c) 244 cm
(b) 255 cm
(d) 55 cm
(b) 2
(d) 4
Q39. If sum of the HCF and LCM of two
numbers is 680 and the LCM is 84 times the
HCF. If one of the number is 56, the other is:
(a) 84
(c) 8
(b) 12
(d) 96
Q40. Three numbers are in the ratio 1 : 2 : 3
and their HCF is 12. The numbers are
(a) 12, 24, 36
(c) 4, 8, 12
(b) 5, 10, 15
(d) 10, 20, 30
Q41. The smallest perfect square divisible by
each of 6, 12 and 18 is
(a) 196
(c) 108
(b) 144
(d) 36
Q42. The number nearest to 43582 divisible by
each of 25, 50 and 75
(a) 43500
(c) 43600
(b) 43650
(d) 43550
Q43. The largest 4-digit number exactly
divisible by each of the 12, 15, 18 and 27 is
(a) 9690
(c) 9930
(b) 9720
(d) 9960
Q44. Find the smallest number of five digits
exactly divisible by 16,24,36 and 54.
(a) 10368
(c) 10300
(b) 10500
(d) 10000
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