HCF and LCM Problems (Advanced)

Q.1. A room is 4 mts 37 cm long and 3 mts 23 cm broad. The floor needs to be paved with a minimum number of square slabs. Find the least number of slabs required for this purpose.
1. 485
2. 431
3. 391
4. 381
5. 415
Q.2. Find the greatest number which will divide 3959, 4082 and 4164 leaving the same remainder in each case.
1. 30
2. 45
3. 41
4. 43
5. 47
Q.3. Find the greatest number which will divide 1063 and 1403 leaving the remainder 9 in each case.
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1. 48
2. 34
3. 40
4. 42
5. 36
Q.4. A merchant has three different types of milk- 324 litres, 351 litres and 459 litres. Find the minimum number of casks of equal size that can store the milk without mixing.
1. 17
2. 61
3. 42
4. 45
5. 51
Q.5. Find the greatest number which will divide 21, 69 and 93 so as to leave the same remainder in each case.
1. 12
2. 18
3. 24
4. 32
5. 30
Q.6. Find the greatest number that will divide 989, 1258 and 1359 leaving remainders 66, 51 and 10, respectively.
1. 71
2. 81
3. 68
4. 73
5. 77
Q.7. . The traffic lights at three different road crossings change after every 24 sec., 36 sec. and 72 sec. respectively. If they all change simultaneously at 8 : 20 : 00 hrs; then they will again change simultaneously at:
1. 8 : 21 : 12 hrs
2. 8 : 28 : 22 hrs
3. 8 : 27 : 36 hrs
4. 8 : 27 : 48 hrs
5. None of these
Q8. Find the least number which when divided by 6, 12, 16 and 125 leaves 7 as remainder in each case but when divided by 11 leaves no remainder.
1. 8007
2. 13007
3. 11007
4. 18017
5. 18007
Q9. A wholesale coffee dealer has 24 kilograms, 120 kilograms and 72 kilograms of three different qualities of coffee. He wants it all to be packed into various boxes of equal size without mixing. Find the capacity of the largest possible box.
1. 50
2. 36
3. 24
4. 12
5. 45
Q10. Find the least number of five digits which when divided by 4, 25, 12 and51 leaves remainder 8 in each case.
1. 10088
2. 10072
3. 10208
4. 10096
5. None of these
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