How many of the 1st 1200 natural nums r either prime to 6 or to 15

• 1 to 1200
  no. of primes of 6=1200/6=200
  no. of primes of 15=1200/15=80
  LCM of 6,15=30
  no. of primes of 30=1200/30=40
  reqd no.=200+80-40=240
  
• 11 years agoHelpfull: Yes(45) No(2)
• The number of primes to 6 cannot be found directly. If a number is co-prime to 6, it should not be a multiple of either 2 as well as 3.
  For example, 4 cannot be co-prime to 6, as it is a multiple of 2, same is the case with 9.
  Similarly, if a number is prime to 15, it should not be multiple of 3 or 15.
  
  So, in the final answer we should consider the numbers which are not multiples of each of 2, 3 and 5.
  
  So, we have to solve this in terms of venn-diagrams, a three variable venn diagram
  In the diagram one circle denotes the multiples of 2, the other one multiples of 6 and the third one multiples of 5.
  
  Multiples of 2 = n(A) = 1200/2 = 600
  Multiples of 3 = n(B) = 1200/3 = 400
  Multiples of 5 = n(C)= 1200/5 = 240
  Multiples of 2 and 3 = n(A n B) = 1200/6 = 200
  Multiples of 2 and 5 = n(A n C) = 1200/10=120
  Multiples of 3 and 5 = n(B n C) = 1200/15 = 80
  Multiples of 2, 3 and 5 = 1200/30 = 40
  
  So, n( A U B U C) n(A) + n(B) + n(C) - n(AnB)-n(AnC)-n(BnC) + n(AnBnC)= 600+400+240-200-120-80+40 = 880
  
  So, all these numbers ar either multiple of 2, 3 or 5.
  
  So, the remaining numbers that is 1200-880 = 320 are primes with respect to 6 and 15
  
  Some of these numbers in the list are all the primes and composite numbers like 77, 91 and so on
  
  Answer is 320
• 11 years agoHelpfull: Yes(9) No(0)
• Pls tell me which one is right.. !!!
• 11 years agoHelpfull: Yes(4) No(0)
• numbers prime to 6 are=1200(1-(1/2))(1-(1/3))=400
  numbers prime to 15 =1200(1-(1/3))(1-(1/5))=640
  numbers prime to both=1200(1-(1/2))(1-(1/3))(1-(1/5))=320
  therefore total= 400+640-2*320=400.
  This is the correct answer
• 11 years agoHelpfull: Yes(3) No(0)
• It depends on the actual question.
  If it is about co-primes, 320 is the correct answer. As I have seen a similar problem before, i assumed it as co-primes.
  If the question is about multiples of either 6 or 15, then 240 is the right answer.
• 11 years agoHelpfull: Yes(1) No(0)
• I agree with the Kavi Priya on the values except the final answer, it should be
  640+400-320 = 720
  
  So, if we are considering primes of either 6 or 15, which means we are considering a number like 25 in the list because though 25 is not a prime of 15, it is prime to 6, in this case 720 is the answer.
  
  720 is the answer
• 11 years agoHelpfull: Yes(1) No(1)
• i am so confused wd so many asnwers
• 11 years agoHelpfull: Yes(1) No(0)
• i think 400 is the right answer
• 11 years agoHelpfull: Yes(1) No(0)
• 400 is the exact answer
• 10 years agoHelpfull: Yes(1) No(0)
• 1 to 1200
  no. of primes of 6=1200/6=200
  no. of primes of 15=1200/15=80
  LCM of 6,15=30
  no. of primes of 30=1200/30=40
  reqd no.=200+80-40=24
  
  now total no which are prime to 6 or 15 are=1200-240 =960
  am correct ?
  
• 10 years agoHelpfull: Yes(1) No(0)
• please explain which one is the correct answer..??
• 11 years agoHelpfull: Yes(0) No(0)