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Part of 2017 Purple Comet Problems

Problems(2)

Purple Comet 2017 MS Problem 4

Source:

4/14/2018
The following diagram includes six circles with radius 4, one circle with radius 8, and one circle with radius 16. The area of the shaded region is kπk\pi. Find kk.
https://snag.gy/zNPBx0.jpg
Purple Comet
Purple Comet 2017 HS problem 4

Source:

3/19/2020
Find the least positive integer mm such that lcm(15,m)=lcm(42,m)lcm(15,m) = lcm(42,m). Here lcm(a,b)lcm(a, b) is the least common multiple of aa and bb.
LCMnumber theory