simple-maths

PROBLEM SPECIFICATION:
You are given three positive integers 'n' , 'a'  and 'b' . In the given range from 1 to 'n' how many distinct numbers are completely divisible by
'a' or 'b' or both?
NOTE: The range includes both 1 and 'n'.

INPUT SPECIFICATION:
You will be given 't' test cases. Each test case will contain three integers 'n' 'a' and 'b'.

OUTPUT SPECIFICATION:
In a single line print the count of numbers that are divisible by 'a' and 'b'.

CONSTRAINTS:
0<t<100
n<10^15
0 ≤ a<10^6
0 ≤ b<10^6

NOTE: In case,if  'a' or 'b' or both of them are zero,print '-1'   (without quotes).

SAMPLE INPUT
1
24 5 3

SAMPLE OUTPUT
11

Explanation

Here in the given range there are total 11 distinct numbers that are divisible by 5 or 3 or both.

Source: hackerearth | Difficulty: UNKNOWN_DIFFICULTY


Solutions:
def lcm(x, y):
	if x > y:
		 greater = x
	else:
		 greater = y
	while(True):
		 if((greater % x == 0) and (greater % y == 0)):
			  lcm = greater
			  break
		 greater += 1
	return lcm
t = int(input())
for j in range(t):
	 c = 0
	 n,a,b = tuple(map(int,input().split()))
	 if((a == 0) or ( b == 0)):
		  print((-1))
	 else:
		  c = (int(n/a)) + (int(n/b)) -(int(n/(lcm(a,b))))        
		  print(c)