Final answer:
To find the smallest number that satisfies the given conditions, calculate the LCM of the divisors (26, 39, 52, 65) and subtract 4. This solution leverages the pattern that each remainder is 4 less than its divisor.
Step-by-step explanation:
To find the smallest number that leaves specific remainders when divided by different divisors, we need to look for a number that satisfies all the given conditions simultaneously. This problem is typically solved by applying the Chinese Remainder Theorem or by looking for a pattern to determine the smallest number that when divided by each of the divisors results in the given remainders. In this specific case, we can express each condition as an equation:
- Number = 26k + 22
- Number = 39j + 35
- Number = 52i + 48
- Number = 65h + 61
Since each remainder is 4 less than its divisor (e.g., 26 - 22 = 4), we can infer that the same number x added to 4 will be exactly divisible by each of the divisors. This means we are looking for a number x such that:
x + 4 = LCM(26, 39, 52, 65)
We calculate the LCM of the divisors, and then subtract 4 to find the number that satisfies all the given conditions. Keep in mind that the LCM of these divisors might need to be adjusted to match the remainders exactly.