Learn how to find the least common multiple of two or more more numbers.

The least common multiple is the smallest number that two or more numbers will divide into exactly.

Welcome to MooMooMath and finding the least common multiple of two or three numbers. The lcm is the smallest number that is divisible by two or more numbers evenly.

In this example I'm going to use a factor tree.

Let’s begin factoring I will start factoring the 8. I can multiply 2 times four and I will circle the 2 because it is a prime number. Then 4 can be divided into 2 times 2 and I know it is factored because they are both prime numbers.

Next I will factor 42

2 times 21 and circle the prime number 2.Next you have 3 times 7 and they are both prime numbers.

Step 2 is to multiple all of the prime numbers together but you can't have any duplicate numbers.

I will put a check by the prime number 2, and that does it for duplicates. I next just write out all of the prime numbers out and multiply them together for the least common multiple.

I have 2 times 2 times 3 times 7

When I multiply these together I get 2 2 = 4 4 x 2 = 8 and 8 x 3 = 24 and 24 times 7 is 168.

Therefore 168 is the lowest common multiple of 8 and 42.

Let's look at an example with three or more numbers.

We have 6 12 and 36

I will create a factor tree for 6 which is 2 x 3 and it is factored.

Then 2 x 6 and circle the 2 because it is prime.

Then 2 times 3 and it is now factored.

Finally I factor 36

2 goes into 36

You have 2 x18 then 2 x 9 then 3 x 3

Now with three numbers you have to look for duplicates in all three numbers.

First get duplicates for all three numbers.

I have a 2 and 3 are all duplicates.

We have a 3 a 3 and a 3

Now I look for duplicates in any 2 numbers and I have 2

I'm left with a 3.

I then just multiply 2 x 3 = 6 then 6 x 2 = 12 and then 12 times 3 = 36

So 36 is the least common multiple (lcm) of 6, 12, and 36

Finally we have 5 20 and 35.

5 is prime so I will circle 5

20 multiply 2 x 10 then 5 x 2

35 I multiply 5 x 7 and they are both prime.

I next I look for common numbers.

We have a 5 and I then just add the rest of the prime numbers for the lcm.

I multiply 5 x 2 x 2 x7

5 x 2 = 10 10 x 2 = 20 and 20 x 7 = 140.

Therefore, 140 is the lowest common multiple of 5, 20, 35

That is how you find the least common multiple of two or more numbers.

Thanks for watching.

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Tagged under: common multiple,lowest common multiple,lcm,math lcm,fractions,math videos,mathematics

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