# Math Help - Numbers

1. ## Numbers

Given that $132=2^2 \times 3 \times 11$ and $252=2^2 \times 3^2 \times 7$
Use these results to find:

the highest common factor of $132$ and $252$,

the smallest interger $k$ such that $132k$ is a multiple of $252$

2. We have that $\text{lcm}(132,252)\times \text{gcd}(132,252) = 132\times 252$

And we know that: $\text{gcd}(132,252) = 2^2\times 3 = 12$

Hence $\text{lcm}(132,252)/132 = k=..$?

3. hi what is gcd? and sorry... i didnt understand your workings

4. Originally Posted by Punch
Given that $132=2^2 \times 3 \times 11$ and $252=2^2 \times 3^2 \times 7$
Use these results to find:

the highest common factor of $132$ and $252$,

the smallest interger $k$ such that $132k$ is a multiple of $252$
for the hcf look at the common results you get (2^2 and 3)

Times these together so you get 2^2*3=12

The HCF is 12

5. Sorry I have no idea what gcd is either and I don't know of any other way to get the LCM albeit manually.

6. Just found a method for you

Find the prime factors of both

Then, lets say one has prime factors of (making this up) 2x2 and 3x3 and 5 and the other has prime factors of 3 and 5x5 and 7

Now take the numbers from each one which are in most frequency. I know that sounded confusing, sorry.

Look at it this way, the first number has more 2s than the second, so we take 2x2, the first number also has more 3s so we take 3x3 from it but the third number has more 5s and 7s so we take 5x5 and 7 from it.

Multiply it all together and you get the HCF (2x2x3x3x5x5x7)

7. hi what is gcd? and sorry... i didnt understand your workings
Sorry, thought you'd be familiar with these terms.

gcd = greatest common divisor,
lcm = lowest common multiple ( the one you need to find)

There's a theorem that states gcd(n,m)* lcm(n,m)=nm. A very useful thing, since you know what value gcd(n,m) is in this case.

8. Originally Posted by Mukilab
Sorry I have no idea what gcd is either and I don't know of any other way to get the LCM albeit manually.
Hello Mukilab, as for the GCD it's the greatest common divisor.

For instance if you have 3 numbers, a,b and k. And k | a and k | b then k is a common divisor. The greatest common divisor speaks for itself then.. and its written GCD(a,b)

I'll give you an example: