Question

Find the number of positive integer less than 10,000 and are

divisible by 5 or 7?​

Answer 1

this question was based on LCM...

Answer 2

We have to find the positive integer less than 10000 and are divisible by 5 or 7.

solution : divisible by 5 or 7 means divisible by 5 + divisible by 7 - divisible by 35.

case 1 : divisible by 5

5 , 10, 15 , .... 10000

first term, a = 5

common difference, d = 5

last term = 10000

using formula, Tn = a + (n - 1)d

⇒10000 = 5 + (n - 1)5

⇒9995/5 = (n - 1)

⇒n = 1999 + 1 = 2000

case 2 : divisible by 7,

7, 14 , 21 , .... 9996

first term, a = 7

common difference, d = 7

last term = 9996

so, 9996 = 7 + (n - 1)7

⇒9989/7 = n - 1

⇒n - 1 = 1427

⇒n = 1428

case 3 : divisible by 35

35 , 70, 105 ... 9975

⇒9975 = 35 + (n - 1)35

⇒9940/35 = n - 1

⇒n - 1 = 284

⇒n = 285

so total no of possible positive integers less than 10000 and are divisible by 5 or 7 is (2000 + 1428 - 285) = 3143