Number leaving given remainders when divided by several divisors: LCM plus or minus a constant

This type of question, asked 2 times: 3 Feb 2022 Tier II, 7 Mar 2023 Tier II. All 2 questions below, oldest first.

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Question 1
3 Feb 2022 Tier II
26 $The sum of the digits of the least number which when divided by 36, 72, 80 and 88 leaves the remainders 16, 52, 60 and 68, respectively, is:$
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Question 2
7 Mar 2023 Tier II
2 $The largest three-digit number that gives the same remainder 2 when divided by 3, 5 and 9 is ________.$
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