LCM & GCF Lesson

Before we begin our lesson, please take a moment to watch the YouTube video below!

Application of LCM

The traffic light we see on road avidly exercises the concept of LCM and HCF.

the controller of these traffic signals is set in a way that it calculates the timings of the nearby places in the same area and then calculates the LCM of all the traffic stops to set the timing for each signal

Application of LCM and HCF

Encryption
LCM of significant prime integers is also used in RSA encryption methods for safely transmitting data over internet connections.
One way to generate a long key is to use the least common multiple (LCM) and highest common factor (HCF) of two large numbers.

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• "Divide" or "split"

• "Equal parts" or "equal sections"

• "Greatest" or "maximum"

• "Common factor"

• "Shared"

For example, "A farmer wants to divide his field into equal parts. The field is 60 meters by 90 meters. What is the largest possible size for each part?"

GCF

• "Every" - such as "every 2 days" or "every 5 hours" etc.

• "Cycle", "rotation" or "period"

• "At the same time"

• "Together" or "simultaneously"

• "Least" or "minimum"

For example, "Two satellites orbit the Earth every 2 days and 3 days, respectively. When will they both orbit the Earth at the same time?"

LCM

Keywords for Word Problems

Multiple Choice

Two numbers have a GCF of 15 and an LCM of 450. If one of the numbers is 90, what is the other number?

• 5

• 30

• 75

• 1350

Multiple Choice

Given three numbers: 30, 50, and 70. If you pick two numbers at random, what is the probability that their LCM will be 350?

• 1

• $$\frac{1}{3}$$

• $$\frac{1}{2}$$

• 0.2

Multiple Choice

Two numbers have a property such that their LCM is 72 times their GCF. If one of the numbers is 8, determine the other number (assuming the other number has at least one factor of 2 but no higher power of 2)

• 36

• 35

• 34

• 33