Question

How many numbers are there from 300 to 700 which are divisible by 2, 3 and 7?

A) 7 B) 8 C) 9 D) 10

Answer 1

Answer:

i think answer is C. 9...

Step-by-step explanation:

Hope its help you

Answer 2

Correct Question:

How many numbers are there from 300 to 700 which are divisible by 2, 3 and 7?

Answer :

Option c) 9

Explanation:

A number which should be divisible by 2 , 3 and 7 must be the multiple of their LCM .

LCM of 2, 3 and 7 is 47.

Hence, any number to be divisible by 2 , 3 and 7 will be the multiple of 42 .

So the multiple pf 42 nearest 300 is 336 .

And then other numbers are 378, 320, 462, 504, 546, 588, 630, and 672 and so on....

Now, Let x be the number divisible by 42 from 300 to 700.

Therefore,

$\implies\sf{l = a + (x - 1)d}$

$\implies\sf{672 = 636 + (x - 1)}$

$\implies\sf{ \frac{336}{42} = x - 1 }$

$\implies\sf{x = 8 + 1} \\ \implies\sf{ x = 9}$

Hence, 9 numbers are there from 300 to 700 which are divisible by 2, 3 and 7

Hence, Option C is the Correct Answer!