Question

How many of the first 100 positive integers are divisible by all of the numbers 2, 3, 4, and 5?

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is B 1

We know that,if a number is divisible by $p$ and $q$, then it is also divisible by the LCM of $p$ and $q$.
The LCM of $2,3,4,$ and $5$ is
$2=2\times 1$
$3=3\times 1$
$4=2\times 2$
$5=5\times 1$
LCM of $2,3,4,5=2^2\times 3\times 5=60$
Therefore, $60$ is the only number (less than $100$) divisible by $2,3,4,and5.$