## LCM and HCF Practice Set - 1

1. 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) 8
b) 11
c) 13
d) 16
e) none of these
2. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:
a) 30
b) 22
c) 40
d) 60
e) none of these

3. If the product of two numbers is 2496 and HCF is 8,then the ratio of HCF and LCM is
a) 1:32
b) 39:1
c) 1:39
d) 4:63
e) none of these
4. A gardener had a number of shrubs to plant in rows. At first he tried to plant 8,then 12 and then 16 in a row but he had always 3 shrubs left with him. On trying 7 he had none left. Find the total number of shrubs.
a) 154
b) 147
c) 137
d) 150
e) none of these
5. A rectangular courtyard 140cm long 525cm wide is to be paved exactly with square  tiles, all of the same size. what is the largest size of the tile which could be used for the purpose?
a) 64cm
b) 35cm
c) 21cm
d) 28cm
e) none of these
6. In a seminar the number of participants in Technology, Economics and Science are 150, 90 and 180 respectively. Find the minimum number of rooms required, where in each room the same number of participants are to be seated and all of them being in the same subject.
a) 27
b) 32
c) 30
d) 25
e) none of these
7. What is the HCF of 3/5, 7/10, 2/15, 6/21?
a) 5/123
b) 6/121
c) 2/105
d) 1/210
e) none of these
8. Find the least number which when divided by 10, 15, 18 and 30 leaves remainders 6, 11, 14 and 26 respectively.
a) 72
b) 86
c) 85
d) 90
e) 94
9. Find the least number which when divided by 2, 3, 4 and 5 leaves a remainder 3. But when divided by 9 leaves no remainder?
a) 33
b) 63
c) 81
d) 123
e) None of these
10. HCF and LCM of two numbers is 5 and 275 respectively and the sum of these two numbers is 80. Find the sum of the reciprocals of these numbers
a) 16/125
b) 32/275
c) 32/125
d) 16/275
e) None of these
11. The traffic lights at three different road crossings change after every 40 sec, 72 sec and 108 sec respectively. If they all change simultaneously at 5 : 20 : 00 hours, then find the time at which they will change simultaneously.
a) 5 : 28 : 00 hrs
b) 5 : 30 : 00 hrs
c) 5 : 38 : 00 hrs
d) 5 : 40 : 00 hrs
e) 5 : 42 : 00 hrs
12. A rectangular courtyard 4.55 meters long and 5.25 meters wide is paved exactly with square tiles of same size. Find the largest size of the tile used for this purpose?
a) 25 cm
b) 45 cm
c) 21 cm
d) 35 cm
e) None of these
13. 5 bells commence tolling together and toll at intervals 2, 4, 6, 8 and 10 seconds respectively. Find in 40 minutes, how many times do they toll together?
a) 8 times
b) 19 times
c) 21 times
d) 30 times
e) 28 times
14. John, Smith and Kate start at same time, same point and in same direction to run around a circular ground. John completes a round in 250 seconds, Smith in 300 seconds and Kate in 150 seconds. Find after what time will they meet again at the starting point?
a) 30 min
b) 25 min
c) 20 min
d) 15 min
e) 23 min
15. If the sum of two numbers is 55 and the HCF and LCM of these numbers are 5 and 120 respectively, then the reciprocals of the numbers is equal to:
a) 45/123
b) 907/34
c) 11/120
d) 56/117
e) 83/149