# Least Common Multiple

Question:

What is the smallest 5-digit common multiple of 32, 36 and 40?

My method:

1. LCM of the given numbers is taken.
2. LCM in first step divides the least 5-digit number,10,000.

How should I proceed further?

Or is there any other way?

First take the lcm of the three numbers, this will give you 1440. Then divide $10000$ by this number $10000/14400=6.94$. So the smallest five-digit number that is divided by the three numbers is the result of the previous division (rounded to the next integer) times the lcm. $7 \cdot 1440 = 10080$.