LCM of (a,18) is 36, HFC=2. Find a
Answers
Answer:
6 is the required answer
Step-by-step explanation:
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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.