Question

1 p
10
If 'a' and 'b' are two positive integers,
then HCF(a,b) * LCM(a,b) =​

Answer 1

Answer:

ab

Step-by-step explanation:

HCF(a,b) * LCM(a,b) =​a×b

As

Let p be a prime. If p occurs in a with multiplicity m and in b with multiplicity n, then it will occur in the LCM of a and b with multiplicity max(m,n) and in their HCF with multiplicity min(m,n).

Hence, in the product of LCM and HCF the multiplicity of p is

max(m,n)+min(m,n)=m+n,

which is also the multiplicity of p in a⋅b. Since this holds for every p, the two products must be equal.

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