LCM ‑ ASSESSMENT 1

Summary

In this script, a manufacturing plant produces 60 gears and 75 screws per hour, and the manager is trying to determine the minimum time in which both gears and screws will be produced in the same quantity. The solution involves calculating the least common multiple (LCM) of 60 and 75, which gives the time when both quantities will be equal. The LCM of 60 and 75 is 300, meaning after 5 hours, the plant will have produced the same number of gears and screws. The correct answer to the question is 5 hours.

Takeaways

• 😀 The script involves a manufacturing plant that produces gears and screws.
• 😀 The plant produces 60 gears per hour and 75 screws per hour.
• 😀 The manager needs to find when the production quantities of gears and screws will be the same.
• 😀 The script highlights the problem of determining the minimum time for equal production of gears and screws.
• 😀 The question asks how many hours it will take for the number of gears and screws to be the same.
• 😀 The given options for the number of hours are 4, 5, 10, 15, or 'not available'.
• 😀 The script suggests the need for a mathematical approach to solve the problem.
• 😀 The manager is looking for the least common multiple (LCM) of the production rates of gears and screws.
• 😀 The gears and screws are produced at different rates (60 per hour vs. 75 per hour).
• 😀 The problem involves finding the time when both production rates will result in equal quantities.
• 😀 The solution requires calculating the minimum time based on the LCM of 60 and 75.

Q & A

What type of production does the manufacturing plant specialize in?

The manufacturing plant produces gears and screws.

How many gears does the plant produce per hour?

The plant produces 60 gears per hour.

How many screws does the plant produce per hour?

The plant produces 75 screws per hour.

What is the goal of the manager in this scenario?

The manager needs to find the minimum time in which both gears and screws will be produced in the same quantity.

What method is suggested for finding when the number of gears and screws will be the same?

The least common multiple (LCM) of 60 and 75 is used to find when both gears and screws will be produced in the same quantity.

What is the LCM of 60 and 75?

The LCM of 60 and 75 is 300.

How do you calculate the time at which the number of gears and screws will be the same?

The LCM (300) is divided by the production rate for both gears (60) and screws (75).

What is the time it will take for the gears to be produced in the same quantity as screws?

It will take 5 hours for the gears and screws to be produced in the same quantity.

How does the production rate of gears affect the time to reach an equal quantity with screws?

The rate of 60 gears per hour means that it will take 5 hours (300 ÷ 60) to reach the same quantity as 75 screws per hour.

What would happen if the plant produced 100 gears per hour instead of 60?

If the plant produced 100 gears per hour, the time to produce the same quantity of gears and screws would decrease, and the LCM would be different.