The problem involves finding the product of the Highest Common Factor (HCF) and the Lowest Common Multiple (LCM) of two numbers, given their ratio and the difference between them.
Solving HCF LCM Ratio and Difference
Let the HCF of the two numbers be $H$ and the LCM be $L$.
We are given that the ratio of HCF to LCM is 1:30. This can be written as:
$ \frac{H}{L} = \frac{1}{30} $
This implies that $L = 30H$.
We are also given that the difference between the LCM and HCF is 493:
$ L - H = 493 $
Calculating HCF and LCM
Substitute $L = 30H$ into the difference equation:
$ 30H - H = 493 $
$ 29H = 493 $
Now, solve for $H$:
$ H = \frac{493}{29} $
$ H = 17 $
So, the HCF is 17.
Now, calculate the LCM using $L = 30H$:
$ L = 30 \times 17 $
$ L = 510 $
The LCM is 510.
Finding the Product of LCM and HCF
The question asks for the product of the LCM and HCF.
Product = $L \times H$
Product = $510 \times 17$
Product = $8670$
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Important Questions from LCM and HCF
Six bells begin to toll together and toll, respectively, at intervals of 3, 4, 6, 7, 8 and 12 seconds. After how many seconds, will they toll together again?
A and B are two prime numbers such that A > B and their LCM is 209. The value of A 2 - B is:
Find the least number which when divided by 12, 18, 24 and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
Calculate the HCF of \(\frac{12}{5}\) , \(\frac{14}{15}\) and \(\frac{16}{17}\) .
Three numbers are in the proportion of 3 : 8 : 15 and their LCM is 8280. What is their HCF?
