What number is divisible by 7 and 9 and in between 200 and 300?

Answer 1

First, compute the least common multiple of 7 and 9.

lcm(7,9) = (7*9)/gcd(7,9) where gcd(7,9) is the greatest, common divisor of 7 and 9, that is the largest number that divides both numbers. In this case, the gcd is 1.

So, lcm(7,9)=7*9=63

So we want to find a multiple of 63 between 200 and 300

Note that 63 < 300-200 = 100. So we must be able to find a number in between 200 and 300 that is a multiple of 63.

Now we divide 200 by 63 to get 3.174603....

Since 200/63 = 3.174603 < 4 (rounding up to the nearest integer)

It follows that 200/63 < 4

and then 200 < 63*4

Since 7, and 9 both divide 63, it follows they both divide 63*4

So the answer is: 252