A natural number when divided by 3, 4, 5, 6 and 7 respectively, leaves corresponding reminders of 2, 3, 4, 5 and 6.What is the smallest of all such numbers fulfilling the above condition? [1] 2519 [2] 419 [3] 209 [4] 839

A natural number when divided by 3, 4, 5, 6 and 7 respectively, leaves corresponding reminders of 2, 3, 4, 5 and 6.What is the smallest of all such numbers fulfilling the above condition?

[1]  2519    [2] 419     [3] 209       [4] 839

Answer :-

[2] 419

Here 

3 – 2 = 1, 4 –3 = 1, 5–4 =1,  6-5=1,  7-6= 1  

∴ The required Number is  = LCM of (3,4, 5, 6,7) – 1
= 420 – 1 = 419.
Hence option [2] is correct answer.