Question

in the question find the no between 800 to 900 which is divisible by 22, 33 and 66. i know that the answer is 858 but why should we multiply 66 by 13

Answer 1

Answer :

To find number between 800 to 900 which is divisible by 22 , 33 and 66 .We find LCM of 22 , 33 and 66

22 = 2 $\times$ 11

33 = 3 $\times$ 11

And

66 = 2 $\times$ 3 $\times$ 11
So,
LCM ( 22 , 33 and 66 = 2 $\times$ 3 $\times$ 11 = 66
And

all multiples of 66 is divisible by 22 , 33 and 66 .

We know

66 $\times$ 10 = 660 ( That is not lies between 800 and 900 ) ,

66 $\times$ 11 = 726 ( That is not lies between 800 and 900 ) ,

66 $\times$ 12 = 792 ( That is not lies between 800 and 900 ) ,

66 $\times$ 13= 858 ( That is lies between 800 and 900 ) ,

66 $\times$ 14 = 924 ( That is not lies between 800 and 900 ) ,

So,

Our number 858 is divisible by 22 , 33 and 66 and lies between 800 and 900 .