There are seven thieves:They steal Diamonds from a diamond merchant and run away in jungle. While running , night sets in and they decide to rest in the jungle. When everybody is sleeping , two of the best friends get up and decide to distribute the diamonds among themselves and run away. So, they start distributing but find that one diamond was extra. So, they decide to wake up 3rd one and divide the diamond again.... Only to their surprise, they still find one diamond extra. So they decide to wake up the fourth one. And again one diamond is spare.5th woken up ..still one extra. 6th still one extra. now they wake up 7th and diamonds are distributed equally..So, How many minimum number of diamonds did they steal??

minimum no of diamond is 721.

yes he is correct, answer is 301

Lets say there are x diamonds, now these diamonds are exactly divisible by 7.
and
x = 1 + R1*2;
x = 1 + R2*3;
x = 1 + R3*4;
x = 1 + R4*5;
x = 1 + R5*6;
x = R6*7;
where R1, R2, R3, R4 and R5 are integers.
From above we can also say
R1*2 = R2*3 = R3*4= R4*5 = R5*6 = y

Now y should be divisible by 2, 3, 4, 5 and 6, its nothing but common multiple of all.

LCM of 2, 3, 2*2, 5, 2*3 => 2*3*2*5 => 60

at the same time common multiple + 1 should be divisible by 7 as well.

60 + 1 is not divisible by 7
120(60*2) + 1 is not divisible by 7
180(60*3) + 1 is not divisible by 7
240(60*4) + 1 is not divisible by 7
300(60*5) + 1 is divisible by 7

Thus they must have stolen minimum 301 diamonds

301 is the answer and there are many solutions possible.among them least value is 301.in general the no.(60k+1) if divisible by 7 then all r the solutions

answer is 301... minimum number of diamonds are {integer multiple of (LCM(2,3,4,5,6) )+1} so we have to select the integer in such a way that the number is exactly multiple of 7. So the answer is 301.

We need remainder 1 when divided by 2,3,4,5,6. So find LCM of them. We get 60. Now 60+1=61 but 61 is not divisible by 7. So have go by trial and error method only. Multiple of 60 +1 should be divisible by 7.So 61, 121,181,241,301.... Among these 301 is divisible by 7So least required number is 301..Now LCM of 2,3,4,5,6 and 7 is 420301 + 420 = 721 (property of factors)721 + 420 =11411141 + 420 = 1561...