Final answer:
Using the product of the HCF and LCM to find the second number, we divide the LCM by the given first number to get the second number: 2µ7³ / 2· = 2³ 7³. Hence, option D, 2³ 7³, is the correct answer.
Step-by-step explanation:
The question asks to find the other number when one of two numbers is known, along with their Highest Common Factor (HCF) and Least Common Multiple (LCM). The HCF is given as 2µ and the LCM as 2µ7³. One of the numbers is 2·.
To find the other number, we can use the relationship between two numbers (let's call them A and B), their HCF, and LCM, which is HCF × LCM = A × B. Here A is 2·, HCF is 2µ, and LCM is 2µ7³. Substituting the values we get 2µ × 2µ7³ = 2· × B. Simplifying, we get B = 2µ7³ / 2· = 2⁸(2µ)7³ / 2·
= 2⁻²7³ = 2³ 7³.
Therefore, the other number is 2³ 7³, which is option D.