Question

How many natural numbers between 1 and 900 are NOT multiples of any of the numbers 2, 3, or 5?

• A. 240
• B. 250
• C. 270
• D. 300
• E. 210

Answer 1

The correct option is A 240

Note: This is based on the concept of Euler’s number

A number N can be written as $a^m{b}^n$. In this case, $N=900=2^2\times 3^2\times 5^2$

The question can be rephrased as

The number of natural numbers which are less than 900 and relatively prime to it is

$N=[1-\left(\frac{1}{a}\right)][1-\left(\frac{1}{b}\right)][1-\left(\frac{1}{c}\right)]$

$N=[1-\left(\frac{1}{2}\right)][1-\left(\frac{1}{3}\right)][1-\left(\frac{1}{5}\right)]=240$