Aptitude - Problems on H.C.F and L.C.M - Discussion

3:4:5 was arrived at, by cancelling the greatest common factor (How? say we have 3 no.s 100,200,300. To write them in the ratio form we would cancel the greatest common factor from all these three no.s which is 100, to give us the ratio - 1:2:3).

Therefore, the numbers we are looking for in the question, are- hcf*3, hcf*4, hcf*5.
We are given that the LCM of these numbers is 2400, i.e LCM(hcf*3, hcf*4, hcf*5) = 2400
So,
n1 = hcf * 3,
n2 = hcf * 4,
n3 = hcf * 5,

Therefore, LCM = hcf*3*4*5 (LCM is the least no. that IS DIVIDED COMPLETELY by all three numbers).
thus,
hcf *3*4*5 = 2400.
hcf = 40.

Then the numbers are 120, 160 ,200 [ratio 3:4:5 holds, LCM - 2400 holds].

Please if you don't mine reply what is mean by co-prime?

Can anyone say if instead H.C.F is given in place of L.C.M.

And asked to find L.C.M?

600,800,1000 commom divisor is :200

600)800(1
600
---------
200)600(3
600
---------------
0
---------

200)1000(5
1000
-------
0
----------


so 200 is the H C F.............

In the explanation answer,the formula has been used is
Factor of number 3x={3,x}
Factor of number 4x={4,x}
Factor of number 5x={5,x}
Therefore,LCM is a product of {3,4,5,x} [x has taken once as it is common] i.e.LCM=60x
60x=2400
x=40
But,
If we take another formula that
Product of all numbers = Product of LCM and HCF
3x*4x*5x=2400*x
60x3[x to the power 3 or x cube]=2400x
x3[x to the power 3 or x cube] 2400
------------------------------ = ------
x 60
x2[x to the power 2 or x square]=40

therefore, x= square root of 40
then?
Can anybody solve my query???

@shrimant....

The formula works only for two number..for eg take num
2,4,8....hcf is 2

lcm is 16.

product of hcf and lcm=32

product of num=64.

Easy method
3*4*5 = 60
2400/60 = 40

If given HCF what can I do. ?

If h.c.f is given then just do 3*4*5=60 and then 6o*40(h.c.f given)=2400

Better way to find hcf for three numbers is either you could take the differences between them respectively.