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Question
In an apartment consisting of 108 floors, two lifts A and B starting from the ground floor, stop at every 3rd and 5th floors respectively. On which floors, will both of them stop together?
Solution
Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105
Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105
Common multiples of 3 and 5 are 15, 30, 45, 60, 75, 90 and 105
Both the lifts will stop at floors 15, 30, 45, 60, 75, 90 and 105
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