3 and 30.
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2 and 20
HCF of 3 means that the two numbers share 3 as a prime factor. LCM of 30 means there is a 2, a 3 and a 5 as prime factors between the numbers. With this info, we can have the combination where one number has a 2 and the other a 5 (and both have the 3) or one number has just the 3 and the other has 2, 3 and 5. Thus the 2 numbers can be 6 and 15. Or they can be 3 and 30.
To find the LCM, you multiply the numbers together and then divide by the HCF. In this case, we don't know the numbers, but we have the HCF (13) and we have the product of the numbers (1690). Thus all you do is divide 1690 by 13 to get: 1690/13 = 130 And thus the LCM of two numbers whose hcf is 13 and product is 1690 is 130.
2 and 30 6 and 10
The HCF of both numbers is 2