A number when divided by 14 or 13 leaves a remainder 3. Find the least possible value of that number?
Find the LCM of 13 and 14, then add 3
Where a and b are integers
3 + 13*a = x
3 + 14*b = x
Subtract one line from the other:
14*b = 13*a
smallest integers that satisfy that are 14, 13.
so:
3 + 13*14 = x
3 + 14*13 = x
x = 185
To find the least possible value of the number, we need to find the least common multiple (LCM) of 14 and 13, and then add the remainder of 3 to it.
To find the LCM of two numbers, we can list out their multiples until we find a common multiple.
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, ...
Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, ...
We can see that the least common multiple of 14 and 13 is 182.
Now, we add the remainder of 3 to 182: 182 + 3 = 185.
Therefore, the least possible value of the number is 185.