Find the number of combinations of a,b,c if LCM of ab =1000,LCM of bc =2000 and ca is 2000

• LCM (a, b) = 2^3×5^3
  LCM (b, c) = 2^4×5^3
  LCM (c, a) = 2^4×5^3
  
  Calculation for powers of 2:
  Maximum power of 2 is 4 in c. and either a or b will take 3 and other will take 0, 1, 2, 3.
  
  Case 1:
  c = 4, a = 3, b = 0, 1, 2, 3
  4 options
  
  Case 2:
  c = 4, b = 3, a = 0, 1, 2
  3 options (we have used a = 3 in case 1)
  
  Total options for 2 powers = 7
  
  Calculation for powers of 5:
  Maximum power of 5 is 3. So any 2 of a, b, c have maximum power 3. and other will take 0, 1, 2, 3
  
  Case 1:
  a = 3, b = 3, c = 0, 1, 2, 3
  4 Options
  
  Case 2:
  a = 0, 1, 2; b = 3; c= 3,
  3 options
  
  Case 3:
  a = 3; b = 0, 1, 2; c = 3
  3 Options
  
  Total options for 5 powers = 10
  
  therefore, Total options are 7 x 10 = 70
• 9 years agoHelpfull: Yes(4) No(2)
• 1000=2^3*5^3 here we geot 10 combination,
  2000=2^4*5^3 here we got 12 combination,
  similarly for ca we got 12 combination,
  so total no. of combination =10+12+12=34.
• 9 years agoHelpfull: Yes(0) No(7)
• ab/bc=a/c=1/2
  ac=2000
  dividing by c^2 both side
  ac/c^2=2000/c^2
  a/c=2000/c^2 => 1/2=2000/c^2
  c^2=2*2000
  c=20*(10)^1/2
  
  according to question
  bc=ca
  b=a
  a=b=10*(10)^1/2
• 9 years agoHelpfull: Yes(0) No(2)