Number Theory questions – LCM HCF

Few more questions on LCM and HCF on Number Theory

1. How many pairs of integers (x,y) exist such that the product of x, y and HCF (x,y) = 1080?

2. Find the smallest number that leaves a remainder of 4 on division by5, 5 on division by 6, 6 on division by 7, 7 on division by 8 and 8 on division by 9?
3. There are three numbers a,b, c such that HCF (a,b) = l, HCF(b,c) =m and HCF (c,a) = n. HCF(l,m) = HCF(l,n) = HCF(n,m) =1. Find LCM of a,b,c. (The answer can be “This cannot be determined”).

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