Question
The HCF and LCM of two numbers, A and B, are 9 and 162,
respectively. The difference between these two numbers is 27. Find their sum.Solution
ATQ,
HCF (A, B) = 9
LCM (A, B) = 162
We know that,
HCF (A, B) × LCM (A, B) = A × B
Also, A – B = 27
Or, B = A – 27
ATQ:
A × (A – 27) = 9 × 162
Or, A² – 27A = 1458
Or, A² – 27A – 1458 = 0
Or, A² – 54A + 27A – 1458 = 0
Or, A(A – 54) + 27(A – 54) = 0
Or, (A – 54)(A + 27) = 0
So, A = 54 or A = -27
Since, A cannot be negative, we discard A = -27.
So, A = 54
And, B = 54 – 27 = 27
Therefore, required sum = (54 + 27) = 81
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