Question 63

Find the smallest natural number 'x' that must be subtracted from 1800 so that (1800- x), when divided by 7, 11, and 23, will leave 5 as the remainder in each case.

Solution

Here the divisor numbers are 7, 11, and 23.

So the LCM of (7, 11, 23) = $$7\times11\times23$$ = 1771

As in the question, it is given that when 1800 is subtracted from 'x', then divided by 7, 11, and 23 leaving 5 as a remainder in each case.

1771+5 = (1800-x)

1776 = (1800-x)

x = 1800-1776

Smallest natural number 'x' = 24

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