Question

HCF of two numbers is 6, their LCM is 72 and one of the numbers is 18. What is the other number

Answer 1

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.

Answer 2

Answer:

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