Question

Let x be the smallest number greater than 400 which gives the remainders 2, 3 and 4, when divided by 5, 6 and 7, respectively. Find x:​

Answer 1

Question :- Let x be the smallest number greater than 400 which gives the remainders 2, 3 and 4, when divided by 5, 6 and 7, respectively. Find x ?

Solution :-

Checking difference between numbers and remainders first, we get,

→ (5 - 2) = (6 - 3) = (7 - 4) = 3 = Let k.

Than,

→ Required least number will be = LCM of (5, 6 and 7) - k .

So,

Prime Factors of 5,6 and 7 :-

→ 5 = 1 * 5

→ 6 = 2 * 3

→ 7 = 1 * 7

LCM = 5 * 2 * 3 * 7 = 210 .

But , we have given that, Number must be greater than 400.

So,

→ Next factor of LCM will be = 210 * 2 = 420 .

Hence,

→ Required number = (Factor of LCM) - k = 420 - 3 = 417. (Ans.)

∴ Value of x will be 417.

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