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Find the least number which when divided by 16, 36 and 40 leaves 5 as remainder ineach case. |
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Answer» Answer: The answer to this one is 5 more than the LCM of 16, 36 and 40. To find the LCM, break down each of the numbers into its prime factors. Thus 16 = 2 x 2 x 2 x 2, so the LCM will have to have at LEAST four factors of 2; SIMILARLY, 36 = 2 x 2 x 3 x 3 and 40 = 2 x 2 x 2 x 5, so the LCM will also have to have at least two factors of 3 and a single 5. Gathering the necessary factors, we get the LCM of 2 x 2 x 2 x 2 x 3 x 3 x 5 = 720. Adding 5 (the remainder from each division), we get 725. CHECKING, 725 = (16 x 45) + 5 = (36 x 20) + 5 = (40 x 30) + 5. |
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