Question
What is the largest three-digit
number that leaves a remainder of 5 when divided by both 11 and 13? Call this number a. Additionally, what is the smallest four-digit number that is divisible by both 32 and 38? Call this number b. Determine the difference between b and a.Solution
ATQ, If a number leaves the same remainder when divided by two different numbers, then the number is the sum of a multiple of the two divisors and the remainder. Since, 11 × 13 = 143 And, 999 ÷ 143 ~ 6.98 So, largest 3 digit number that is multiple of 11 and 13 = 143 × 6 = 858 So, x = 858 + 5 = 863 Since, 'Q' is divisible by both 32 and 38. So, it must divisible by L.C.M of 32 and 38 = 608 So, smallest possible 4 digit number that is multiple of 608 = 608 × 2 = 1216 Therefore, required difference = 1216 - 863 = 353
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