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Write a complete pseudo-code of a program which adds all numbers that are multiples of both 7 and 9 up to 600.?
Wiki User
∙ 14y ago
Since 7 and 9 are relatively prime, any number that is a multiple of both is a multiple of 7 x 9 = 63. There are 9 multiples of 63 less than or equal to 600, so this can be computed directly using Sum = 63(1 + 2 + ... + 9) which simplifies to Sum = 63 x 9 x (1 + 9)/2 from the formula for arithmetic series.
Most programming languages have a built-in function which returns the quotient and the remainder when dividing integers, or you can write your own. So to generalize, denote 600 by max, 7 by a, and 9 by b. Input those values first. Suppose quotient returns the quotient of an integer division.
begin
N <- quotient(max, lcm(a,b)) (* N is the number of multiples of both a and b <= max *)
sum <- lcm(a,b) * N * (1 + N)/2 (* Use the formula *)
end
This is the most efficient solution. There are other solutions that don't assume an understanding of arithmetic series. Specifically, you could write:
begin
i <- 1; sum <- 0 (* Initialize counter to 1 and sum to 0 *)
While i <= max/lcm(a,b) do
sum <- sum + i * lcm(a,b)
i++;
od
end
Wiki User
∙ 14y ago
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