If the prime factorisation of a and b are a - 22- 3- x and b - 2- 32- y - 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

Since product of two numbers = LCM × HCF (2^2× 3× x) × (2× 3^2× y) nbsp;=(2× 3× 5) × (2^2× 3^2× 5^2) which gives xy = 5 × 5^2 Therefore either x = 5 and y = ...

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Byju's Answer

Standard X

Mathematics

Product of Two Numbers = HCF X LCM of the Two Numbers

If the prime ...

Question

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? ( $x \neq 1, y \neq 1$ )

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 $x y = 5 \times 5^{2}$
Therefore either x = 5 and y = 25 or x = 25 and y = 5.
We cannot specify respective values. But, we can say that the sum is always 25 + 5 = 30.

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If the prime factorisation of a and b are a=22×3×x and b=2×32×y ; 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 = 30Since product of two numbers = LCM × HCF (22×3×x)×(2×32×y)=(2×3×5)×(22×32×52) which gives xy=5×52 Therefore either x = 5 and y = 25 or x = 25 and y = 5. We cannot specify respective values. But, we can say that the sum is always 25 + 5 = 30.

If the prime factorisation of a and b are $a = 2^{2} \times 3 \times x$ 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? ( $x \neq 1, y \neq 1$ )