1, 107.
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107 is a prime number but 117 is a composite number
One hundred seven.
Well, darling, the numbers between 61 and 107 that are multiples of 3, 5, and 10 are... drumroll please... 60 and 90. Yep, just those two bad boys fit the bill. So, go ahead and give 'em a round of applause for being the chosen ones in that range.
103, 107, 109, 113.
Since all numbers between 61 and 107 are less than 367, none of them are divisible by 367. 84 is a multiple of 3, 6 and 7 in that range.