There is an integer which is divided by 4 leaves a remainder of 1 and divided by 5 leaves a remainder of 2 and divided by 7 leaves a remainder of 2.
Find the number closest to 500 among those integers.
Answer
457
Solution
Such a integer which is divided either by 5 or 7 leaves a remainder of 2 is the integer which 2 is added to the least common multiple of 5 and 7, it is 35 + 2 = 37.
Since 37 = 4 × 9 + 1, 37 is such an integer as it is divided by 4 leaves a remainder of 1.
Thus, the least integer applicable to three conditions is 37.
The number following 37 is a number which the least common multiple of 4, 5, and 7 or 140 is added to 37.
It is 37 + 140 = 177.
In order to find the number closest to 500, look for such an integer N applicable to the formula, 37 + 140 × N = 500. N = (500 - 37) / 140 = 3.3 ....
The suitable number to N is 3.
The integer to find is 37 + 140 × 3 = 457.
Find the number closest to 500 among those integers.
Answer
457
Solution
Such a integer which is divided either by 5 or 7 leaves a remainder of 2 is the integer which 2 is added to the least common multiple of 5 and 7, it is 35 + 2 = 37.
Since 37 = 4 × 9 + 1, 37 is such an integer as it is divided by 4 leaves a remainder of 1.
Thus, the least integer applicable to three conditions is 37.
The number following 37 is a number which the least common multiple of 4, 5, and 7 or 140 is added to 37.
It is 37 + 140 = 177.
In order to find the number closest to 500, look for such an integer N applicable to the formula, 37 + 140 × N = 500. N = (500 - 37) / 140 = 3.3 ....
The suitable number to N is 3.
The integer to find is 37 + 140 × 3 = 457.
