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

HCF is highest factor present in both numbers. Eg: HCF of 8,12 is 4.

Now this HCF must be multiplied with another number to get the the reqd number i.e 4*2 and 4*3.

LCM is least common number that we can obtain by multiplying some other number with the numbers we have. LCM of 8,12 is 24. i.e 8*3 and 12*2. LCM will also have the HCF in it. So, LCM = HCF * other factors, there will only be 2 other factors.

Now LCM*HCF = Product of numbers i.e 4*24 = 8*12; (4*2)*(4*3) = 8*12.

I am partially understood. Can anyone explain clearly the basics?

No more verification needed, its clear, if you look carefully comment of "@Vijay pandey".

Please clearly explain all the concepts of lcm and hcf?

"HCF*LCM=Product of two numbers".

The above expression is universal.

When we calculate hcf of two numbers we find factors which are common.

And for lcm we take common factor and the remaining factors of two.

Here it is given that the other factors of lcm are 13 and 14

So numbers are hcf*lcm part

=>23*13 and 23*14 so 23*14 is greater.

Example: suppose we have two numbers 12 and 15.
Factor of 12=2*2*3.
Factor 0f 15=3*5.
So hcf =common factor=3.
And lcm=2*2*3*5=60 .
lcm part of 12=2*2.
lcm part of 15=5.
If we multiply these lcm parts by hcf we get the corresponding numbers.

H.C.F of two numbers is 23(which is a common factor for both).

So the two numbers will be 23X , 23Y.

L.C.M*H.C.F = 23X*23Y.

Therefore L.C.M will be 23*x*y.

But the other two factors given are 13, 14.

So x will be 13 and y will be 14.

The numbers are 23X, 23Y which are 23*13, 23*14.

The greatest number is 23*14 = 322.

H.C.F. = 23 and L.C.M. are 13 and 14. So if HCF is 23 then two numbers can be 23x and 23y And as given LCM are 13 &14 we know HCF*LCM=x*y so from that 23*13 and 23*14 are two number and greater one is 23*14.

@poornima.

Well explained.

hcf*lcm = n1*n2 = N1(let n1*n2=N1 for lcm=13).

Case1:
23*13=N1;

similarly,
Case2:
23*14=N2;(n1*n2=N2 for lcm=14).

So N2>N1.

The other solution is the bigger number is 23x7x13 and smaller number is 23x2.

These numbers also will have hcf as 23 and lcm as 23x13x14.