Basic Math Least Common Multiple

This next lesson is on finding the least common multiple.0000

To review, a multiple is a number or the numbers that the original number can multiply into.0008

If I have a number 4, the multiples would be 4, 8, 12, 16, 20, and so on.0016

Multiples would be numbers that the original number can multiply into.0033

The least common multiple is known as the LCM; we are comparing two numbers.0044

From the multiples of the two numbers, we are going to find the smallest common multiple.0055

In order to do this, there is two methods that we can use.0065

The first method is to simply list out the multiples of each number.0069

You are going to find the smallest one.0076

For 6, the multiples would be 6, 12, 18, 24, 30, 36, 42, 48.0082

I am going to just stop there for now.0111

List out the multiples of 10; for 10, 20, 30, 40, 50, and 60.0115

If you look at this, from these numbers, a common multiple is 30.0136

If I were to keep going, for the 6, this would be 54 and 60.0146

Another common multiple would be 60.0154

But again I want to find the least common multiple.0158

It is going to be the smallest common multiple which is 30.0162

The LCM of 6 and 10 would be 30.0168

Another method to finding the LCM is going to involve prime factorization.0176

If you don't remember prime factorization, you can go back to that lesson and just review over that.0185

I am going to find all the prime factors of 6 and 10.0196

To do that, I have to use a factor tree.0201

6, I am going to break down into 3 and 2.0204

Circle them because they are prime numbers.0210

10, the factor pairs of 10 would be 5... 5 is a factor... and 2.0214

That is also prime; I circle it.0229

Look at the prime factors of 6, 3 and 2.0233

I look at the prime factors of 10 which is 5 and 2.0238

I look for any common factors; the common factor between 6 and 10 is 2.0242

If I list this out, 6 is 3 and 2.0249

The prime factors of 10, 5 and 2; they have a common factor of 2.0257

When they have a common factor, I am going to take one of them and cross it out.0264

Cross out only one of them.0273

Then I take all the remaining numbers--3, 5, and then this 2.0276

I am going to multiply them out.0281

The LCM is going to be 3 times 5 times 2 which is equal to 30.0285

Whichever method you would like to use, you will still get the same answer of 30.0300

Let's find the LCM of 12 and 15; you can pause it.0311

I want you to try to use both methods to find the LCM.0317

Then just come back and we will go over it.0323

12 and 15; I am going to use the second method for all these examples.0328

I am going to use the factor tree method to find all the prime factors of these numbers.0337

For 12, I can use a factor pair of 6 and 2.0344

Or I can use 4 and 3.0349

3 is a prime number; I am going to circle it.0354

4, I am going to break up into two prime numbers, 2 and 2.0357

I circle those numbers.0363

For 15, the factor pair would be 5 and 3.0365

These are both prime numbers; I am going to circle them.0373

For 12, all the prime numbers would be 2 times 2 times 3.0377

The prime factorization of 15 is 5 and 3.0387

I look for any common numbers between 12 and 15.0393

They have a common number of 3.0399

I am just going to take one of them and cross it out.0401

These are common; there is a 2 here and a 2 here.0407

But that is within the same number, 12.0411

I don't want to cancel that out.0413

It has to be one from here and one from the other number.0415

I am going to take the remaining numbers--2, 2, 5, and 3.0418

I am going to multiply them out.0424

My LCM is going to be 2 times 2 times 5 times 3.0428

This is going to be 4; this is going to be 15.0438

My answer is 60.0446

The next example is finding the LCM of 16 and 20.0458

Let's use the factor tree; the factor pair of 16 would be 4 and 4.0466

You can also use 8 and 2; circle them because they are prime.0474

2 and 2, circle those numbers.0484

For 20, I can use 10 and 2; or I can use 5 and 4.0489

5 is a prime number; I am going to circle that one.0498

4 becomes 2 and 2; circle those.0501

For 16, the prime factorization would be 2 times 2 times 2 times 2.0509

For 20, 5 times 2 times 2.0522

Look at this; we have a common number here.0532

I am going to cancel one of these out; it doesn't matter which one.0535

That took care of that pair.0541

We have a 2 here and another 2 here, another common number.0543

Again I am going to cancel out one of them.0548

I am going to leave the other one.0551

You are going to take all the remaining numbers--2, this 2, 5, 2, including this one, 2.0554

I am going to multiply them all out.0564

The LCM is going to be 2 times 2 times 5 times 2 times 2.0567

This is 2 times 2; this is 4; times 10 times 2.0583

You are going to get 80 as your answer.0592

Example three, let's use 15 and 25.0603

The prime factors of 15, 5 and 3; for 25, we have 5 and 5.0615

I can write them out; then for 25.0631

They have a common number of 5.0644

I am going to cancel out one of those factors.0646

Even though I have a 5 here and a 5 here,0652

I am not going to cancel that out because they are both in the same number, 25.0654

I take the remaining numbers.0660

My LCM is going to be the product of those numbers.0664

3 times 5 times 5; my answer is going to be 75.0669

For this example of 12 and 18, we are going to find the LCM, the least common multiple.0691

In order to do that, I am going to use the factor tree method0699

to find all the prime factors which is the second method that we went over.0702

12, I am going to use the factor pair 4 and 3.0708

I can also use 6 and 2.0716

This is a prime number; I am going to circle this.0719

For 4, break this up into 2 and 2.0722

They are both prime; I am going to circle them.0729

Then do the same thing for 18.0733

For 18, I can use 9 and 2; or I can use 6 and 3.0736

This is a prime number; circle that one.0743

For 6, I am going to use 2 and 3.0747

Circle them because they are prime.0752

For 12, all the prime factors are going to be 2, 2, and 3.0755

For 18, 2 times 3 times another 3.0767

I am going to look for any common factors between 12 and 18.0775

I know that there is a common factor of 3 for both 12 and 18.0780

I am going to take one of the numbers and just cross it out.0787

Just cancel one of the numbers out.0790

I also have a common factor of 2; 2 and 2.0794

I am going to take that and cancel one of those out.0801

Even though I have a 2 here and a 2 here, they are within the same numbers.0806

I am not going to cancel that out.0811

I take all the remaining numbers--this one, this one, and these two.0814

I am going to multiply them out to find the least common multiple.0823

It is going to be 2 times 2 times 3 times 3.0828

I am going to get 4 times 9 which is going to be 36.0837

The least common multiple of 12 and 18 is 36.0848

Thank you for watching Educator.com.0854