Question

find the smallest number which when dividedby 72 and 90 leaves no remainder
​

Answer 1

Answer:

You need to be really careful with how you word these questions.

First, I will answer your question how you asked it, and then I will answer your question how I think you might have meant to ask it.

You asked: “What is the smallest number, which when divided by 72 and 90, leaves no remainder?”

Thus the number, x, must be divided by 72, and divided by 90, and the result should be 1.

(x/72)/90 = 1

x/72 = 90

x = 6480

6480 is the smallest number that can be divided by both 72 and 90.

Now let me answer the question I think you were trying to ask: “What is the smallest number that is divisible by both 72 and 90?”

This number is 360.

360/72 = 5, and 5 is whole.

360/90 = 4, and 4 is whole.

Additionally, 4 and 5 have no common multiple, so this is the smallest number that can be found.

Divisibility is a property—a number either has it or doesn’t have it. This question prompts first if the number is divisible by 72. Then, it prompts if the number is divisible by 90. If both are true, then the number is divisible by 72 and 90.

Dividing is a verb—an action, it’s something you do to a number. So, to divide a number by both 72 and 90 asks nothing about its property of divisibility