Question 629179: Find the smallest five digit no which when divided by 42 , 56 & 70 leaves exactly three as a reminder Answer by 303795(602) (Show Source):
You can put this solution on YOUR website! Find the smallest number which each of the numbers divides into.
Firstly find the prime number factors for each number
42 = 2 x 3 x 7
56 = 2 x 2 x 2 x 7
70 = 2 x 5 x 7
Write down the numbers and cross off any number which is written as a factor on the other numbers as well.
The lowest common multiple will be 2 x 2 x 2 x 3 x 5 x 7 = 840
The smallest 5 digit number is 10000.
Divide 10000 by 840 and get 11.9
The first multiple of 840 greater than 10000 will be the 12th i.e. 12 x 840 = 10080
So a remainder of 3 will result if the original number was 10083.
10083/42 = 240 remainder 3
10083/56 = 180 remainder 3
10083/70 = 144 remainder 3
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