Question

How many numbers are There To Between 1000 and 12000 which are divisible By both 21and 32.​

Answer 1

Answer:

First number after 500 and divisible by 13 = 507 and number just less than 1000 and divisible by 13 = 99

So, there are 38 numbers between 500 & 1000 which are divisible by 13.

Answer 2

First and foremost we have to find out the LCM of 21 and 33.

21 = 3 × 7

33 = 3 × 11

∴ LCM of 21 and 33

= 3 × 7 × 11

= 231

231 is divisible by both 21 and 33 .

The numbers between 1000 and 12000 which are divisible by both 21 and 33 are

1155 , 1386, . . . , 11781

we have to Count the numbers

The numbers 1155 , 1386, . . . , 11781 forms an arithmetic progression

First term = a = 1155

Common Difference = d = 231

Let number of terms in the AP = n

Then nth term of the AP = 11781

a + ( n - 1 )d = 11781

⇒ 1155 + ( n - 1 ) × 231 = 11781

⇒ 1155 + 231n - 231 = 11781

⇒ 231n + 924 = 11781

⇒ 231n = 10857

⇒ n = 47

Thus there are 47 numbers between 1000 and 12000 which are divisible by both 21 and 33.

Ans :- There are 47 numbers between 1000 and 12000 which are divisible by both 21 and 33.

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