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The values of x and y are 99 and 343
The HCF of numbers is the highest common factors of the numbers
The LCM of numbers is the lowest common multiple of the numbers
The HCF and the LCM are given as:
[tex]HCF = 21[/tex]
[tex]LCM = 1617[/tex]
Multiply the HCF and the LCM
[tex]HCF \times LCM = 21 \times 1617[/tex]
[tex]HCF \times LCM = 33957[/tex]
The product of the numbers x and y equals the product of the HCF and the LCM.
So, we have:
[tex]x \times y = 33957[/tex]
Express 33957 as a prime factor
[tex]x \times y = 3^2 \times 7^3 \times 11[/tex]
Rewrite the equation as
[tex]x \times y = 99 \times 7^3[/tex]
[tex]x \times y = 99 \times 343[/tex]
By comparison:
[tex]x = 99[/tex]
[tex]y= 343[/tex]
Hence, the values of x and y are 99 and 343
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