The relationship between L.C.M and H.C.F is that:
a * b = L.C.M * H.C.F
Now, if we know any of the three values, we can find the other.
But, in our question there seems that the values are not provided (though they are). We are given the product of a and b (3000) which will work too.
Question No. 11:
Solution:
As we know, a * b = L.C.M * H.C.F
Substituting the value of a, b and the H.C.F in the equation.
3000 = L.C.M * 10
3000/10 = L.C.M
L.C.M = 300
Hence, the L.C.M is equal to 300.
Question No. 12:
We shall use the above equation to solve this one too.
Solution:
As we know, a * b = L.C.M * H.C.F
Substituting the value of a (we can also put b instead of a, it will work too) and the L.C.M and H.C.F in the equation.
160 * a = 1760 * 32
160a = 56320
a = 56320/160
a = 352
Hence, the other number is equal to 352.
Question No. 13:
This one is the same as question no. 11. The only difference is that instead of the H.C.F the L.C.M is given. This one will be easy too as same as question 11.
Question No. 14:
This one got me thinking for a while (nice question). The answer is there in the question itself.
Solution:
As we know, a * b = L.C.M * H.C.F
By substituting the value of the L.C.M and H.C.F in the equation, we get:
a * b = 300 * 20
Since we have only two values, we can solve this by comparing the two sides.
a * b = 300 * 20
⇒ a = 300 and b = 20
Proof:
300 * 20 = 300 * 20
6000 = 6000
This means it is true (and will always be true in such cases.)
Extra: If your getting more curious try to check whether the L.C.M and H.C.F of 600 and 40 are 600 and 40 respectively :) (you will always end up right with any numbers you try)
I hope my answer helped :)
