# Gcf of 9 18 and 27 relationship

### Relationship between H.C.F. and L.C.M. | Highest common Factor | Solved Examples

the list 1, 2, 3, 6, the set of common factors. Since 6 is the The Greatest Common Factor is the largest whole number that divides evenly two F54 = {1,2, 3,6,9,18,27,54}. Thus, .. (g) What is the relationship between a and b if LCM(a,b ) = a? 8. Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27 Common multiples of 2 and 3 include 6, 12, 18, and How to find the greatest common factor. The greatest common factor of two or more whole numbers is the 1, 2, 3, 6, 9, 18, 27, and

These same procedures can be done with any set of two or more non-zero whole numbers. A common multiple of two or more nonzero whole numbers is a whole number that a multiple of all of them.

### Least common multiple (video) | Khan Academy

The lowest common multiple or LCM of two or more whole numbers is the smallest of their common multiples, apart from zero.

Hence write out the first few common multiples of 12 and 16, and state their lowest common multiple. Hence write down the LCM of 12, 16 and 24?

Solution a The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96,,… The multiples of 16 are 16, 32, 48, 64, 80, 96,,… Hence the common multiples of 12 and 16 are 48, 96, ,… and their LCM is Two or more nonzero numbers always have a common multiple — just multiply the numbers together. But the product of the numbers is not necessarily their lowest common multiple. What is the general situation illustrated here? Solution The LCM of 9 and 10 is their product The common multiples are the multiples of the LCM You will have noticed that the list of common multiples of 4 and 6 is actually a list of multiples of their LCM Similarly, the list of common multiples of 12 and 16 is a list of the multiples of their LCM This is a general result, which in Year 7 is best demonstrated by examples.

In an exercise at the end of the module, Primes and Prime Factorisationhowever, we have indicated how to prove the result using prime factorisation. This can be restated in terms of the multiples of the previous section: One is the prime factorization approach.

## Least common multiple

We can take the prime factorization of both of these numbers and then construct the smallest number whose prime factorization has all of the ingredients of both of these numbers, and that will be the least common multiple.

So let's do that. So we could write 18 is equal to 2 times 3 times 3. That's its prime factorization. So 12 is equal to 2 times 2 times 3. Now, the least common multiple of 18 and let me write this down-- so the least common multiple of 18 and 12 is going to have to have enough prime factors to cover both of these numbers and no more, because we want the least common multiple or the smallest common multiple.

So let's think about it. Well, it needs to have at least 1, 2, a 3 and a 3 in order to be divisible by So let's write that down. So we have to have a 2 times 3 times 3. This makes it divisible by If you multiply this out, you actually get And now let's look at the So this part right over here-- let me make it clear.

**Greatest Common Factor 18 and 12 TEK 6.1E**

This part right over here is the part that makes up 18, makes it divisible by And then let's see. Well, we already have one 3, so our 3 is taken care of. We have one 2, so this 2 is taken care of. But we don't have two 2s's. So we need another 2 here.

### The Greatest Common Factor | Help With Fractions

So, notice, now this number right over here has a 2 times 2 times 3 in it, or it has a 12 in it, and it has a 2 times 3 times 3, or an 18 in it. So this right over here is the least common multiple of 18 and If we multiply it out, so 2 times 2 is 4. And we are done.

Now, the other way you could've done it is what I would say just the brute force method of just looking at the multiples of these numbers.

You would say, well, let's see.