The way to work this out is to break the number down into its prime factors. In this case, 10 can be expressed as 2x5. Thus two numbers will have 10 as a common multiple if the only unique factors between them is a single 2 and a single 5. This can be achieved with the following pairs:
1 and 10
2 and 10
5 and 10
2 and 5
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5,65,7
1 and 30 is one possible answer.
4 and 9 22 and 23 37 and 53
2 and 15 10 and 15
There are many common multiples of 120 and 149. A common multiple is simply a multiple of both numbers. The least common multiple is 120x149, since 149 is prime. (Note: this trick doesn't work on all pairs of number. Although the product is always a multiple, it's not the least common multiple.)