If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Class 7>Unit 2

Lesson 4: Word problems on HCF and LCM

# GCF & LCM word problems

Here we have a couple of word problems--one searching for the least common multiple and the other for the greatest common factor. Just read them with us slowly and follow along. You'll get it. Created by Sal Khan.

## Want to join the conversation?

• Isn't the LCM of 8 and 6 going to be 24?
8*1 = 8 6*1 = 6 6*4 = 24
8*2 = 16 6*2 = 12
8*3 = 24 6*3 = 18
• Can HCF or LCM be negative?
• No, HCF and LCM need to be positive at all times.
• What is the different between gcf and lcm
• Factors and multiples are opposites of each other.
For example:
Multiples of 15 are: 15, 30, 45, 60, 75, etc.
Factors of 15 are: 1, 3, 5, and 15

Now, how do these apply to GCF and LCM.
Let's find the GCF of 15 and 9
Prime factors of 15 = 3 * 5
Prime factors of 9 = 3 * 3
The 2 numbers share one common factor. The GCF = 3.

Now, let's find the LCM for 15 and 9
Multiples of 15: 15, 30, 45, 60, 75, ...
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, ...
The first common multiple (LCM) = 45

Hope this helps.
• "Umaima just bought 1 package of 21 binders. She also bought 1 package of 30 pencils. She wants to use all the binders and pencils to create identical sets of office supplies for her classmates."

Wouldn't the greatest number of sets be 21? 1 binder with 1 pencil in each set? Yes there would be pencils left over but who cares?
• I agree with your premise but what matters is what the problem asked for. It does say "She wants to use ALL the binders and pencils".
• At , Sal says that the LCM can be calculated using prime factorization, and I am fluent in the method. I do not use the first method employed in the video's first problem.
So can I rely on prime factorization for all LCM problems in my test (which is an online multiple-choice test, where the method of calculation doesn't matter as I'll only calculate on rough sheets of paper)?
• Yes, you could use prime factorization for all LCM problems, and it would always work if you use the method correctly. The method involves using each prime factor the greatest number of times it occurs in any of the prime factorizations.

However, for some problems, this method is not always the most efficient method. Efficiency might matter if your test is timed. For example, if one of two numbers is a multiple of the other number, then the LCM of the two numbers is the larger number (for example, because 24 is a multiple of 8, LCM(8,24) is 24). Also, if two numbers have only 1 as a common factor, then the LCM of the two numbers is their product (for example, LCM(9,10) is 9*10=90, because the only common factor of 9 and 10 is 1).
• What's the main difference between gcf and Lcm?
• Here's an example that might clarify things for you.

Let's find the common multiple of 6 and 4
Multiples of 6 are: 6, 12, 18, 24, 30, ...
Multiples of 4 are: 4, 8, 12, 16, 20, 24, ...
The LCM = 12. This is the 1st multiple that they have in common.
You may also see this referred to as LCD = Lowest Common Denominator.

Now, look at common factors.
Factors of 6: 1, 2, 3, 6
Factors of 4: 1, 2, 4
A lowest common factor would = 1 for all numbers.
The Greatest Common Factor (GCF) or Greatest Common Divisor (GCD) = 2. This is the largest number that you can divide evenly into both 4 and 6.

Hope this helps.
• Why is it so HARD? and compicated
• Because you don't undestand it very well. Keep working on it and suddenly you'll reilize how simple it really is.
• When can you tell when it's going to be GCF or LCM?
• Some ways you can tell is for GCF, the problem will ask for the GREATEST amount of something while for LCM, the problem will ask for the LEAST amount of something.
• i don't get the video
• Factors are For example what can go into nine? Well 9x1 and that is one, 3 goes itno nine beacause 3x3 is 9. so our little chart is 1,3,9,, lets just stop there okay! Now to make it simple for the next thing which is you guessed it commen multipules, is pretty simple it is like a times table chart so you would go 9 x1= 9 2x9=18 3x9=27 And so on forth, lets take a look at what we have for cm well 9,18,27. Her eis a trick to remeber the nines
09
18
27
36
45
54
63
72
81
90
I so hope this helps!