Question
Download Solution PDFIf the LCM of four distinct numbers is 270 and the HCF of each pair is 9, then what is the product of the four numbers?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
LCM of four numbers = 270
HCF of each pair is 9
Calculation:
According to the question, the HCF of each pair is 9
⇒ The four numbers will be 9a, 9b, 9c and 9d
[Where a, b, c and d are random numbers]
⇒ LCM (9a, 9b, 9c and 9d) = 9 × (abcd)
According to the question, LCM = 270
⇒ 9 × (abcd) = 270
⇒ (abcd) = 30
Now, the product of four numbers = 94 × (abcd)
⇒ Product of four numbers = 6561 × 30 = 196830
∴ The product of the four numbers is 196830.
Alternate Method
Given:
The LCM of four distinct numbers is 270.
The HCF of each pair is 9.
Concept:
LCM = Products of four numbers × HCF
Calculation:
Let the four numbers be a, b, c, and d.
The HCF of each pair is 9.
Then, the four numbers are 9a, 9b, 9c, and 9d.
LCM = Products of four numbers × HCF
⇒ 270 = abcd × 9
⇒ abcd = \(270\over9\) = 30
Products of the number = 9a × 9b × 9c × 9d
⇒ 94 × abcd
⇒ 6561 × 30 = 196830
∴ The product of the four numbers is 196830.
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