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Question

If HCF of two numbers is 6 and lcm of two same two numbers is 72.Find the numbere


Solution

LCM×HCF=Product of two numbers

Since their HCF is 6, let the numbers be 6m and 6n

Now apply the formula. (Also note that m and n are coprime, i.e. gcd(m,n)=1

You'll get :

6m×6n=6×72⟹mn=12  ; m,n∈N 

Now the possible unordered pairs of (m,n)are :

(1,12);(2,6);(3,4)

Out of which only the pair (3,4) is coprime.

Hence, the numbers are : 18 and 24


Mathematics

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