Factors & Multiples Problem Sum
In this lesson, we will learn how to solve HCF and LCM problem sums effectively. One of the main challenges students face is deciding whether a question requires the use of HCF or LCM when presented in a word problem. This lesson introduces a clear, common-sense approach to help students identify the correct method to apply with confidence.
Students will first work through four examples that focus on recognising whether to find the HCF or LCM for each problem. After that, two of these examples will be explored in greater detail, with step-by-step explanations to deepen understanding and reinforce correct problem-solving strategies.
Related Lessons:
How To Identify Whether To Find HCF or LCM?
First, we will learn how to decide whether a problem sum requires the Highest Common Factor (HCF) or the Lowest Common Multiple (LCM). This lesson focuses on a clear, logical approach rather than memorising rules.
- If the answer is expected to be smaller than the smallest number given, we find the HCF.
- If the answer should be larger than the largest number, we find the LCM.
For example, for the following problem sums, we will find the HCF since we expect a value smaller than the smallest value:
- How many square tiles do we need to fill a room size of 120cm by 200cm?
- Find the largest possible number of groups if 150 boys and 20 girls are to be divided equally.
And, for these problem sums, we will find the LCM since we are looking at a future value, which is larger than the largest value:
- 3 lights flash at 3 second, 5 second and 8 second, and first flash together at 1200hrs. When will they flash together again?
- 3 drivers can complete one round of the track in 60 seconds, 120 seconds and 140 seconds. If they start together, when will all three drivers meet again?
Problem Sum Example 1
In this first example, we will find out how many square tiles are needed to cover a room measuring 120 cm by 200 cm.
Solution:
Since each tile cannot be larger than 120 cm—the smaller of the two dimensions—we need to determine the HCF to find the largest possible size of each tile.
First, we will break down 120 and 200 as product of its prime factors.
\(120 =2^3\times3 \times5\)
\(200=2^3\times5^2\)
To find the HCF, we select the common factor and select the smallest. There, the HCF is \(2^3\times5=40\)
Problem Sum Example 2
In the second example, 3 lights flash at intervals of 3 seconds, 5 seconds, and 8 seconds, with their first flash occurring together at 12:00 hrs. When will they flash together again?
Solution:
To find out when they will flash together again, we note that the next common flash must occur after 8 seconds, which is the largest number, so we will need to find the LCM of the three intervals.
Now, expressing 8 as a product of its prime factors:
\(8 =2^3\)To find the LCM, we select all the numbers and select the largest. Therefore:
LCM\(=2^3\times3 \times5=120\) seconds
Since 120 seconds is 2 minutes, therefore, the lights will flash together again at 1202hrs.
Watch Full Concept Breakdown With Examples
For students who prefer step-by-step video explanations, here is the full video lesson covering all the concepts taught above, in a clear and systematic manner.