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Three luminous signs come on at different time intervals. The first lights up every 12 s, the second lights up every 30 s and the third every 24.> If at first they are all lit at the same time, after how many seconds will all three turn on again at the same time? |
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Answer» When such a problem is presented, what we’re looking for is the Least Common Multiple (LCM) of all these numbers. The LCM is the smallest number that has all of these three numbers among its factors, or, the smallest number that is a multiple of all three of these numbers. The way to calculate the LCM of a set of numbers is to first list out all the Prime Factors of the numbers: 4 = 2 x 2 5 = 5 6 = 3 x 2 Then, you multiply each prime FACTOR to the power of the maximum AMOUNT of times it occurs in any one number. For example, 2 appears once for 6, and twice for 4, HENCE 2 appears a maximum of 2 times. Thus, the LCM can be given by [math]2^2[/math] x [math] 3^1 [/math]x [math] 5^1[/math] , which is 4 x 3 x 5. Hence, the LCM will be 60, which MEANS the LIGHTS will next flash together after 60 seconds. |
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