Question : The LCM of two numbers is five times their HCF. If the product of the two numbers is 20480, then find their HCF and LCM, respectively.
Option 1: 46 and 230
Option 2: 48 and 240
Option 3: 64 and 320
Option 4: 56 and 280
Correct Answer: 64 and 320
Solution :
The LCM of two numbers is five times their HCF. If the product of the two numbers is 20480, then find their HCF and LCM, respectively.
LCM o two numbers = 5 × HCF
Product of two numbers = 20480
We know the product of two numbers = Product of their HCF and LCM
According to the question,
Product of two numbers = LCM × HCF
⇒ 20480 = 5 × HCF × HCF
⇒ $\frac{20480}{5}$ = (HCF)
2
⇒ 4096 = (HCF)
2
⇒ (64)
2
= (HCF)
2
⇒ HCF = 64
⇒ LCM = 5 × HCF
⇒ LCM = 5 × 64
⇒ LCM = 320
Hence, the correct answer is 64 and 320.
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