Answered

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x and y are both bigger than 30. x and y have HCF 21 and LCM 1617. Find x and y.

Sagot :

MrRoyal

The values of x and y are 99 and 343

The HCF

The HCF of numbers is the highest common factors of the numbers

The LCM

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]

Prime Factors

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

Read more about HCF and LCM at:

https://brainly.com/question/420337

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