1 and 5.
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These numbers are divided by 5 without remainder, so their common factor must be divided by 5 without remainder aswell. Let's start from 45 stepping over 5 and skipping any unmatching result: not 45, not 40, not 35, not 20 (since none of 45 and 70 divide these without reminder), but it's 15 (which gives us 45/15 = 3 and 70/15 = 5, here both results are round numbers, which gives us 15 as the answer).
35 is not the LCM of 3 and 5, 15 is. LCM means Lowest Common Factor. To find the LCM of 3 and 15 you have to list the multiples: 3, 6, 9, 12, 15, 18, 21 etc. 5, 10, 15, 20, 25, etc. The LCM is the least common number in both the lists, which is 15.
15 and 21 21 and 35
3 and 5 both go into multiples of 15, as both numbers are factors of 15. In mathematical terms, 15 is a multiple of both 3 and 5 because it can be evenly divided by both numbers without leaving a remainder.
The numbers that go into 35 are 1, 5, 7, and 35. The numbers that go into 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000.