Question

LCM of (a,18) is 36, HFC=2. Find a​

Answer 1

Answer:

6 is the required answer

Step-by-step explanation:

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Answer 2

Answer:

If you have intuition on what HCF and LCM are then this is fairly a simple one.

For any two integers : product of the two integers IS EQUAL to product of their LCM and HCF.

now in our scenario :

a x 18 = 36 x 2

a = 4.

If you want the proof for this, then you should know about prime factorization first.

Proof :

For suppose A and B are two integers and they can be prime factorized as following : (x= multiplication; ^ = power; p, q, r, s are prime numbers)

A = p x p x p x q x q x q x q x r x r = p^3 x q^4 x r^2

B = p x p x q x s = p^2 x q x s

then HCF = p x p x q = p^2 x q

and LCM = p x p x p x q x q x q x q x r x r x s = p^3 x q^4 x r^2 x s

now compare A x B and HCF x LCM. Are they equal ? :)

Hope this helps.