Question

There are $4$ numbers. The HCF of each pair is $7$ and the LCM of all the numbers is $1470$. What is the product of the $4$ numbers?

• A. $504210$
• B. $502410$
• C. $504120$
• D. $501420$

Answer 1

The correct option is A

$504210$

Determine the correct option

The Explanation for the correct option:

Option (A):

Given HCF of each pair of numbers $=7$

Let the numbers be $7\mathrm{a},7\mathrm{b},7\mathrm{c},7\mathrm{d}.$

LCM of the four numbers without taking the HCF of the four numbers is equal to the product of the four numbers and HCF

$\mathrm{LCM}=\mathrm{Product}\mathrm{of}\mathrm{four}\mathrm{numbers}\times \mathrm{HCF}$

Substituting the values of HCF, LCM, and the four numbers without HCF in the above formula for finding the LCM, we get

$\begin{array}{rcl}1470& =& \mathrm{a}\times \mathrm{b}\times \mathrm{c}\times \mathrm{d}\times 7\\ \mathrm{a}\times \mathrm{b}\times \mathrm{c}\times \mathrm{d}& =& \frac{1470}{7}=210\end{array}$

Product of the numbers $=7^4\times \mathrm{abcd}$

$=504210$

Hence option(A) is the correct answer.

The explanation for the incorrect option:

Option (B):

1. In this question, we have to use the formula of the product of four numbers without taking the highest common factor and HCF is equals to LCM.
2. Then use the given conditions and values given in the question, and substitute the values of HCF and LCM in the given formula for LCM, to find the required value. But the required value does not match.

Hence the option (B) is incorrect

Option (C):

1. Product of four numbers without taking the highest common factor and HCF is equal to LCM.
2. Substitute the values of HCF and LCM in the given formula for LCM, to find the required value does not match with the given option.

Hence the option (C) is incorrect

Option (D):

1. Use the formula of the product of four numbers without taking the highest common factor and HCF is equal to LCM.
2. Use the given conditions and values given in the question, and substitute the values of HCF and LCM in the given formula for LCM, to find the required value. But the required value does not match.

Hence the option (D) is incorrect

Hence from the calculation It has arrived that the product of the four numbers is $504210$.

So the Correct option is (A).