The smallest number which leaves remainders 22, 35, 48, and 61 when divided by 26, 39, 52, and 65 respectively can be found using the differences between each divisor and its remainder. Here, each difference is 4 (26-22=4, 39-35=4, 52-48=4, 65-61=4). This means the desired number is 4 less than a multiple of 26, 39, 52, and 65. The least common multiple (LCM) of these divisors is 780. Subtracting 4 from 780 gives 776, which is the smallest such number. Hence, the smallest number is 776.