LCM Application Examples

In this class, We discuss LCM Application Examples.

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Example 1:

A, B, and C start simultaneously in the same direction to run around the circular stadium.

A completes a round in 23 seconds, B in 308 seconds, and C in 198 seconds, all starting at the same point.

After what time will they meet again at the starting point?

Solution:

The below diagram helps to understand the concept.

The concept of LCM uses here.

A start at the starting point and come again to the starting point after 252 seconds.

Similarly, B and C come to the starting point after 308 and 198 seconds, respectively.

LCM is the least number divisible by 252, 308, and 198.

LCM(252, 308, 198) = 2772

after 2772 seconds, they meet again at the starting point. Why?

2772/252 = 11 after 11 rounds, A will be at the starting point.

2772/308 = 9. After 2772 seconds B will take nine rounds and reach the starting point.

2772/198 = 14. After 2772 seconds, C will take 14 rounds and reach the starting point.

Example 2:

Four different electronic devices make a beep after every 30 minutes, 1 hour, 1 1/2 hour, and 1 hour 45 minutes, respectively.

All the devices beep together at 12 noon. Will they again beep at?

Solution:

LCM(30, 60, 90, 105) = 1260

The hours are converted to minutes.

After 1260 minutes, they beep again together.

= 21 hours

They beep together at 9:00 am.