On a radio tower, a red light flashes every 6 seconds and a blue light flashes e

游客2024-01-12 49

问题 On a radio tower, a red light flashes every 6 seconds and a blue light flashes every 10 seconds. If both lights flash together at a certain time, how many seconds later will both lights flash together the next time?
______seconds

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答案 30

解析 One way to approach this question is to look at the "flash times" for both lights to see what times they have in common. The following lists show the flash times for both lights as the numbers of seconds after the time at which both lights flashed together.
Red light: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60,…
Blue light: 10, 20, 30, 40, 50, 60, 70, 80, 90, . . .
Note that 30 is the first number that is common to both lists. Therefore, if both lights flash together, they will flash together again 30 seconds later. The correct answer is 30.
Alternatively, you may realize that if the lights flash together, the number of seconds that will elapse before they flash together the next time is the least common multiple of 6 and 10. To find the least common multiple of 6 and 10, begin by writing each integer as the product of its prime factors.
6 =(2)(3)
10 =(2)(5)
Since 2 is a factor in both products, but 3 and 5 are factors of only one of the products, the least common multiple of 6 and 10 is(2)(3)(5), or 30. Therefore, if both lights flash together, the next time they will flash together is 30 seconds later. The correct answer is 30.

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