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

Product of l.c.m and h.cf is that numbers so in the same way hcf is 23 and l.cm 13 and 4 are given and ther the ans 23*14 is right

With this concepts children will not be able to understand as they have been taught in school the other way.

The best solution is,

Since the factors of the lcm of 2 nos are 13, 14 then lcm of the 2 nos will be (13x14) = 182.

This means the lcm of the 2 nos is 182 answer as said that the hcf of the 2 nos is 23.

We know that LCM x HCF = product of the 2 nos.

So 182 x 23 = the product.

So product = 4186.

As factors are 13 and 14.

The nos are 4186/13 = 322 and 4186/14 = 299.

So the bigger of the 2 is 322.

See definitions of H. C. F and L. C. M.
HCF=the product of common factor with least index.
LCM=product of all the prime factor of each of the given num with greatest index.
A/c to given question.
23 is the HCF of TWO given num.
And other two factor 13, 14 of the LCM.
Note :-here 14 is not a prime num hence 14=2*7.
It is clear that 23 is that prime num which is come in the LCM of two number.
Hence total prime number is (2, 7, 13, and 23).
Hence one num is 13*23=299.
And 2nd is=2*7*23.
Answer is (2*7*23).

23 is common in both.

13 and 14 are factors of lcm thus may be common or may occur separate in both number but if they were commen then they should be included into hcf and that is not so.

Therefore 13 and 14 comes separately in both number.

Thus 23*13 and 23*14.

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.

@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.

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.

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.

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.

"HCF*LCM=Product of two numbers".

The above expression is universal.