If the prime factorisation of a and b are a -22- 3 - xb -2 - 32- y andLCM of a- b-22- 32- 52 and HCF of a - b -2 - 3 - 5- which of the following is true- x -1- y -1A- x y-25 B- x-y-30C- x-y-0D- x-6

The correct option is B x + y = 30 Since product of two numbers = LCM × HCF (2^2× 3× x) × (2× 3^2× y) =(2× 3× 5) × (2^2× 3^2× 5^2) which gives xy = 5 × 5^2 So, ...

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Standard VI

Mathematics

Factors

If the prime ...

Question

If the prime factorisation of a and b are

$a = 2^{2} \times 3 \times x$

$b = 2 \times 3^{2} \times y$ and

LCM of (a, b) = $2^{2} \times 3^{2} \times 5^{2}$ and

HCF of (a, b) = $2 \times 3 \times 5$ , which of the following is true? ( $x \neq 1, y \neq 1$ )

xy = 25

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x + y = 30

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x – y = 0

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x = 6

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Solution

The correct option is B
x + y = 30

Since product of two numbers = LCM $\times$ HCF

$(2^{2} \times 3 \times x) \times (2 \times 3^{2} \times y)$

$= (2 \times 3 \times 5) \times (2^{2} \times 3^{2} \times 5^{2})$

which gives $x y = 5 \times 5^{2}$

So, x and y can alternate between the values 5 and 25 and we can not specify respective values. But, we can say that the sum is always 25 + 5 = 30.

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Similar questions

Q. If the prime factorisation of a and b are

a = 2^{2} \times 3 \times x

and

b = 2 \times 3^{2} \times y

; LCM of (a, b) =

2^{2} \times 3^{2} \times 5^{2}

and HCF of (a, b) =

2 \times 3 \times 5

, which of the following is true? (

x \neq 1, y \neq 1

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Q. Question 6
If two positive integers a and b are written as

a = x^{3} y^{2} a n d b = x y^{2}

where x, y are prime numbers, then HCF (a, b) is

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If x = 2³ x 3 x 5², y = 2² x 3², then HCF (x, y) is :

Q. If

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then
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x = \frac{1}{2}, y = \frac{3}{2}

(b)

x = \frac{5}{2}, y = \frac{1}{2}

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If the prime factorisation of a and b are a=22×3×x b=2×32×y and LCM of (a, b) =22×32×52 and HCF of (a, b) = 2×3×5, which of the following is true? (x≠1, y≠1)

The correct option is B x + y = 30 Since product of two numbers = LCM × HCF (22×3×x)×(2×32×y) =(2×3×5)×(22×32×52) which gives xy=5×52 So, x and y can alternate between the values 5 and 25 and we can not specify respective values. But, we can say that the sum is always 25 + 5 = 30.

If the prime factorisation of a and b are

$a = 2^{2} \times 3 \times x$

$b = 2 \times 3^{2} \times y$ and

LCM of (a, b) = $2^{2} \times 3^{2} \times 5^{2}$ and

HCF of (a, b) = $2 \times 3 \times 5$ , which of the following is true? ( $x \neq 1, y \neq 1$ )