Question

Find the least number which when divided by 5, 7 and 13 leaves the same remainder 3 in each case

Answer 1

subtract 3 from all the 3 no.
take the lcm of the outcome i.e. 2 4 and 10
answer is 20

Answer 2

Answer:

The least number that leaves a "remainder 3" when divided by "5, 7 and 13" is 458.

Solution:

Let the least number that is divisible be 5, 7 and 13 be x.

Hence, to find the value of x, we need to find the "lowest common multiple" or "L.C.M." of 5, 7 and 13.

So, L.C.M. of 5, 7 and 13 can be found out as:

∴ L.C.M. = 5 x 7 x 13 = 455 = x

Thus, 455 is the least number that is exactly divisible by all "5, 7 and 13".

So, the least number that leaves a "remainder 3" when divided by "5, 7 and 13" is = x + 3

= 455 + 3

= 458    

Therefore, the least number that leaves a remainder 3 when divided by "5, 7 and 13" is 458.