What is the smallest possible natural number x>5 , that leaves a remainder of 5 whenever it is divided by 14 , 8 or 77
To find the smallest possible natural number that satisfies these conditions, we need to find the least common multiple (LCM) of 14, 8, and 77.
Step 1: Find the multiples of each number until we find a common multiple:
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112...
Multiples of 8: 8, 16, 24, 32, 40, 48, 56...
Multiples of 77: 77, 154, 231, 308, 385, 462, 539, 616...
From the multiples listed, we can observe that 56 is the smallest common multiple of all three numbers.
Step 2: Add 5 to the common multiple to find the smallest number that leaves a remainder of 5 when divided by 14, 8, and 77:
56 + 5 = 61
Therefore, the smallest possible natural number x > 5 that leaves a remainder of 5 when divided by 14, 8, and 77 is 61.