Question

The HCF of two numbers is 29 and other two factors of their LCM are 16 and 19. The larger of the two numbers is
(a) 16
(b)551
(c)19
(d)29​

Answer 1

Answer:

16

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Answer 2

Final Answer:

The larger of the two numbers with their HCF 29 and the other two factors of their LCM 16 and 19, is 551, corresponding to the correct option b.

Given:

The HCF of the two numbers is said to be 29 and other two factors of their LCM are 16 and 19.

To Find:

The larger of the two numbers with their HCF 29 and the other two factors of their LCM 16 and 19, is to be calculated.

Explanation:

The concepts useful in figuring out the solution to this problem here are as follows.

• The Highest Common Factor or HCF is the factor of the highest value that is found to be common to the stated set of numbers.
• The Least Common Multiple or LCM is the multiple of the least value that is found to be common to the stated set of numbers.
• The product of any two numbers is always calculated to be equal to the product of their HCF and LCM.

Step 1 of 3

As per the given statement in the problem, the LCM of the two stated numbers is

$=29\times 16\times 19\\=8816$

Step 2 of 3

Using the information in the given problem, the product of the HCF and LCM of the two stated numbers is

$=29\times 8816\\=255664$

Step 3 of 3

In continuation with the above calculations, some of the probable two numbers are evident from the following calculations.

• $255664=(29\times 29)\times (16\times 19)=841 \times 304$
• $255664=(29\times 19)\times (16\times 29) =551 \times 464$

Taking into consideration the stated options, 551 is evident to be the larger of the two numbers.

Therefore, the required correct answer is option b indicating the number 551.

Know more from the following links.

https://brainly.in/question/54179983

https://brainly.in/question/952029

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