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HCF AND LCM PRACTICE QUESTION



1. The smallest number, which when divided by 5, 10, 12 and 15, leaves remainder 2 in which case; but when divided  by 7 leaves no remainder, is
(1) 189
(2) 182
(3) 175
(4) 91
Ans. 2
2. What least number must be subtracted from 1936 so that the resulting number when divided by 9, 10 and 15 will leave in each case the same remainder 7 ?
(1) 37
(2) 36
(3) 39
(4) 77
Ans. 3
3. The least number which when divided by 18, 27 and 36 separately leaves remainder 5, 14, and 23 respectively, is
(1) 95
(2) 113
(3) 149
(4) 77
Ans. 1
4. The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3 but when divided by 9 leaves no reamainder is
(1) 1677
(2) 1683
(3) 2523
(4) 3363
Ans. 2
5. The greatest number of four digits which when divided by 12, 16, and 24 leave remainder 2, 6 and 14 respectively is
(1) 9974
(2) 9970
(3) 9807
(4) 9998
Ans. 1
6. When a number is divided by 15, 20 or 35 each time the remainder is 8. Then the smallest number is
(1) 428
(2) 427
(3) 328
(4) 338
Ans. 1
7. The smallest number, which when divided by 12 or 10 or 8, leaves remainder 6 in each case, is
(1) 246
(2) 186
(3) 126
(4) 66
Ans. 3
8. The traffic lights at three different road crossing change after 24 seconds, 36 seconds and 54 seconds repectively. 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
Ans. 2
9. From a point on a circular track 5 km long A, B and C started running in the same direction at  the same time with speed of 2_1/2 km per hour, 3 km per hour and 2 km per hour respectively. Then on the starting point all three will meet again after
(1) 30 hours
(2) 6 hours
(3) 10 hours
(4) 15 hours
Ans. 3
10. Four runners started running simultaneously from a point  on a circular track. They took 200 seconds, 300 seconds, 360 seconds and 450 seconds to complete one round. After how much time do they meet at the starting point for the first time ?
(1) 1800 seconds
(2) 3600 seconds
(3) 2400 seconds
(4) 4800 seonds
Ans. 1
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