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HCF and LCM :'(

i swear everywhere i look theres different explanations of how to do it, and none of the ways work. :s-smilie:

i think that for example the hcf of 90 and 175
is 5x5
because prime f of 90= 2x5x3x3 and pf of 175= 5x5x7
so is it 25? because bitesize tells me it's five :s-smilie:

and lcm i dont get at all! how do i work out the lcm of 90 and 175?

Reply 1

hiyaguys

OP

9

anyone? got maths this afternoon ;(

Reply 2

Combustion Chamber

I have maths this afternoon.

HCF = highest common factor , so you simply find the biggest number that goes into both 90 and 175.

So..... Find it :P.

It's basically the same as find the HCF of 20 and 40

2 goes into both
4 goes into both
10 goes into both

But becaus 20 goes into 40 we just say that the HCF of 20 and 40 is 20.

Reply 3

hiyaguys

OP

9

Combustion Chamber

I have maths this afternoon.

HCF = highest common factor , so you simply find the biggest number that goes into both 90 and 175.

So..... Find it :P.

It's basically the same as find the HCF of 20 and 40

2 goes into both
4 goes into both
10 goes into both

But becaus 20 goes into 40 we just say that the HCF of 20 and 40 is 20.

so isnt it 25? bitesize tells me its five :s-smilie:

Reply 4

hiyaguys

OP

9

oh. never mind. got it... i think

Reply 5

saivens

You list all the factors of 90, and then all the factors of 175

I work them out like this
1 x 90
2 x 45
3 x 30
[4 doesn't go into 90]
5 x 18
6 x 15
[7 doesn't go in]
[8 doesn't go in]
9 x 10
[the next number is 10, but we've already got that from 9 x 10]

Then the factors of 175:
1 x 175
5 x 35
7 x 25

So you list them both together:
90 - 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
175 - 1, 5, 7, 25, 35, 175
And then find the highest number in both lists, which would be five.

They should give you an easier one in the exam though, because although HCF is fairly simple, it can take a bit of time.
Do you have your exam this afternoon?

Reply 6

Combustion Chamber

hiyaguys

so isnt it 25? bitesize tells me its five :s-smilie:

It can't be 25 because 40 divided by 25 is not an interger ( whole number ) and besides the HCF has to be lower than 20.

Reply 7

Linda and Suzanne

3

These question often ask you to express one or both of the numbers as a product of prime factors first.

90=2\times 3^2\times 5

175=5^2\times 7

You could write these as

\ \ 90=2^1\times 3^2\times 5^1 \times 7^0

175=2^0 \times 3^0\times 5^2\times 7^1

(I wouldn't normally but it makes it easier to explain on here.)

Now to find the HCF just use the lower power of each prime number.

HCF=2^0 \times 3^0\times 5^1\times 7^0=5

and to find the LCM use the higher power of each prime number.

LCM=2^1 \times 3^2\times 5^2\times 7^1=3150

Reply 8

Oh I Really Don't Care

17

the division algorithm may be of use to you (i.e. it gives you the capability to find both the HCF, LCM)

http://en.wikipedia.org/wiki/Euclidean_algorithm

Using standard notation;

HCF of x and y is represented as (x,y)

The LCM of x and y is represented as [x,y]

Using the above algorithm you can rpove that;

xy = (x,y)[x,y]
So the product of the two numbers is the same as the product LCm and HCF [and you can do some rearangemnt to find the LCM]

In your example;

(90)(175) = 5[90,175]

It follows [90,175] = 3150

Reply 9

KinoJohn

2

Original post by hiyaguys

i swear everywhere i look theres different explanations of how to do it, and none of the ways work. :s-smilie:

i think that for example the hcf of 90 and 175
is 5x5
because prime f of 90= 2x5x3x3 and pf of 175= 5x5x7
so is it 25? because bitesize tells me it's five :s-smilie:

and lcm i dont get at all! how do i work out the lcm of 90 and 175?

Thats is the same problem i`ve encountered with HCM and LCF. Your not the only one who got the answer as 25 instead of 5 as Bitesize says so.

Reply 10

KinoJohn

2

[QUOTE="Suzanne;18856050" Linda="Linda" and="and"]These question often ask you to express one or both of the numbers as a product of prime factors first.

90=2\times 3^2\times 5

175=5^2\times 7

You could write these as

\ \ 90=2^1\times 3^2\times 5^1 \times 7^0

175=2^0 \times 3^0\times 5^2\times 7^1

(I wouldn't normally but it makes it easier to explain on here.)

Now to find the HCF just use the lower power of each prime number.

HCF=2^0 \times 3^0\times 5^1\times 7^0=5

and to find the LCM use the higher power of each prime number.

LCM=2^1 \times 3^2\times 5^2\times 7^1=3150

[/QUOTE

Thanks! That really helped me conquer HCF and LCM!

Reply 11

Mr M

20

Original post by KinoJohn

Thats is the same problem i`ve encountered with HCM and LCF. Your not the only one who got the answer as 25 instead of 5 as Bitesize says so.

You obviously were a bit confused then. You should be able to see immediately that 25 is not a factor of 90.

And was it necessary to bump a thread that has been dead for 4 years?

Reply 12

ShabsKing

Hello bbc bitesize is right as you don't need to multiply 5 as it is only one number in the factors.90=2x5x3x3= 5175=5x5x7=5 if there was one more prime number in 90s prime numbers (extra 5) then you could mutiply it and then 25 would be the hcf I did the same mistake,use mathswatch and then you will understand everything. LCMyou have to take your Hcf which is 5 and multiply with the rest prime numbers of both the numbers;2x5x3x3xx7 including the hcf 5,which is 3,150

HCF and LCM :'(

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