what is the smallest number which will divide by 39, 52, 91, leaves a remainder 13 in each case .
Answers
Answer:
1105
Step-by-step explanation:
answer is correct up to a point. The LCM (Least Common Multiple) is indeed 1092. Adding 13 gives 1105, which is the correct answer. This confirms Dr. Rosenstein’s answer.
I submitted this answer so that there would be at least one answer that showed not only the final result, as Dr. Rosenstein’s answer does, but how it was calculated. Dr. Badarinath Hs’ answer almost did that, by finding the LCM, but instead of taking the final step of adding 13, so that when dividing the total by each of the three given numbers, the remainder would be 13, he incorrectly stated that since all three numbers are divisible by 13, there is no answer. Divisible by 13 they indeed are, but so what? Does that stop us from being able to divide 1105 by each of the three numbers? Of course not (I didn’t say evenly). Does it keep the remainder from being 13? No.
Whenever a number (integer) is divided by a smaller number, the remainder can be any non-negative number less than the divisor (the number by which we divided). When dividing a number larger than 39 by 39, the remainder can be any number from 0 to 38, inclusive, including 13, even though 39 is a multiple of 13. For example, when we divide 14 by 6, we get 2. 6 times 2 is 12. 12 from 14 leaves 2. So the remainder is 2. Hey, how can that be? 6 is divisible by 2. So what? I rest my case.