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3 problems match “Chinese remainder theorem”. Clear

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1. Smallest integer with two remainders ●●○○○ 20 ptsWhat is the smallest positive integer that leaves a remainder of 4 when divided by 5 and a remainder of 6 when divided by 7?
2. Least integer with consistent remainders ●●○○○ 20 ptsWhat is the least positive integer which when divided by 5 gives a remainder of 4, when divided by 6 gives a remainder of 5, when divided by 7 gives a remainder of 6, when divided by 8 gives a remainder of 7, when divided by 9 gives a remainder of 8, and when divided by 10 gives a remainder of 9?
3. Integers with distinct remainders ●●●○○ 50 ptsHow many positive integers at most 420 leave different remainders when divided by each of 5, 6, and 7?