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1.) The smallest positive number which leaves a remainder of 1 when it is divided by 3, 4, 5 or 7 is |
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2.) What is the least number by which 825 must be multiplied in order to produce a multiple of 715? |
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3.) HCF of 4 × 27 × 3125; 8 × 9 × 25 × 7 and 16 × 81 × 5 × 11 × 49 is |
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4.) What is the smallest sum of money which contains an integral number of $2.50, $20, $1.20 and $7.50 each? |
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5.) Find the least square number which is exactly divisible by 4, 5, 6, 15 and 18. |
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6.) Two cyclists are preparing for the Olympics. The first cyclist takes 10 minutes to cover one full round, whereas the second cyclist takes 9 minutes. Find the time when they will both be together at the starting point, if they both start simultaneously. |
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7.) A heap of coconuts is divided into groups of 2, 3 or 5 and each time, no coconut is left over. Find the least number of coconuts in the heap. |
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8.) From 3 drums of milk, 27 L, 33 L and 45 L are to be drawn. To do it in the minimum number of repetitions, the capacity of the measuring can should be |
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9.) An electric wire is sold only in multiples of 1 m and a customer requires several lengths of wire, each 85 cm long. To avoid any wastage and to minimise labour, he should purchase a minimum length of |
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10.) The L.C.M. of two numbers is 360, and their H.C.F. is 12. If the sum of the two numbers is 132, find the difference between the two numbers. |
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11.) The LCM of two numbers is 840, and their HCF is 14. If one of the numbers is 42, find the other number. |
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12.) Three bells ring at intervals of 15 seconds, 20 seconds, and 30 seconds, respectively. If they all ring together at 10:00:00 hours, at what time will they ring together again? |
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13.) Four machines beep at intervals of 20 minutes, 30 minutes, 40 minutes, and 50 minutes, respectively. If they all beep together at 9:00 AM, at what time will they beep together again? |
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14.) If the ratio of two numbers is 5:6 and their H.C.F. is 2, find their L.C.M. |
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15.) Five bells toll at intervals of 5 minutes, 10 minutes, 15 minutes, 20 minutes, and 25 minutes, respectively. If they all toll together at 8:00 AM, at what time will they toll together again? |
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