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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Find the GCF of these numbers: 90, 30

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Find the GCF of these numbers: 14, 70

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Find the LCM of these numbers: 25, 6

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Find the LCM of these numbers: 31, 95

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Find the GCF of these numbers: 63, 18

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Find the LCM of these numbers: 79, 25

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Find the GCF of these numbers: 44, 11

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Find the GCF of these numbers: 60, 32

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Find the LCM of these numbers: 39, 5

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Find the LCM of these numbers: 77, 10

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Find the LCM of these numbers: 30, 39

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Find the LCM of these numbers: 65, 85

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Find the GCF of these numbers: 48, 12, 36

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Find the GCF of these numbers: 36, 96, 48

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Find the GCF of these numbers: 45, 81, 90

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Find the GCF of these numbers: 56, 70, 28

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Find the GCF of these numbers: 78, 91, 13

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Find the GCF of these numbers: 24, 60, 96

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Find the LCM of these numbers: 84, 74, 44

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Find the LCM of these numbers: 5, 6, 94

• "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

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Zoe attends dance practice every 3 days and visits her grandmother every 6 days. If she did both activities today, in how many days will she do both on the same day again?

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Two farmers are cultivating fields of sizes 72 hectares and 90 hectares, and they want to split their fields into plots of equal size for planting different crops, but they want the plots to be as large as possible. What should be the size of each plot?

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Amy and Brian are community volunteers. Amy volunteers every 4 days and Brian volunteers every 6 days. They both volunteered today. When will they next volunteer together?

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A local school has decided to distribute 80 apples and 100 oranges equally among a number of students without splitting any fruit. What is the maximum number of students that can receive the fruits?

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A baker has two types of cookie trays. One tray can hold 6 cookies, and the other can hold 9 cookies. If the baker wants to display the same number of cookies on each tray without breaking any cookies, what is the smallest number of cookies he should bake?

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In a school, there are two clubs: the Science Club and the Math Club. The Science Club meets every 5 days, and the Math Club meets every 7 days. If both clubs meet today, after how many days will they have their meetings on the same day again, given that there's a school holiday on the 35th day and no club meetings will be held on that day?

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Three villages get water supply from the same source. The first village gets water every 8 days, the second village every 12 days, and the third village every 16 days. Due to maintenance, the water supply will be shut down for 3 days after the 40th day. If all villages receive water today, on which day will all three villages receive water together again after the maintenance?

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