Let x be the least number which when divided by 8, 9, 12, 14 and 36 leaves a remainder of 4 in each case, but x is divisible by 11. The sum of the digits of x is .........

Factor of 8 = $$2 \times 2 \times 2$$

Factor of 9 = $$3 \times 3$$

Factor of 12 = $$3 \times 2 \times 2$$

Factor of 14 = $$2 \times 7$$

Factor of 36 = $$2 \times 2 \times 3 \times 3$$

LCM of 8, 9, 12, 14 and 36 = $$2 \times 2 \times 2 \times 3 \times 3 \times 7$$ = 504

Possible number = 504 + remainder = 504 + 4 = 508

but it is not divisible by 11.

Another possible number = 504 $$\times$$ 2 + remainder = 1008 + 4 = 1012

It is divisible by 11.

Sum of number = 1 + 0 + 1 + 2 = 4