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HCF and LCM

Multiple Choice Questions

41.

Product of two co-prime numbers is 117. Then their LCM is

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42.

Find the maximum number of trees which can be planted 20 m apart on the two sides of a straight road 1760 m long.

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43.
The greatest common divisor of
$3 to the power of 3 to the power of 333 end exponent space plus space 1$ and $3 to the power of 3 to the power of 334 end exponent space plus space 1$ is

$3 to the power of 3 to the power of 333 end exponent space plus space 1$

20

2

1

$3 to the power of 3 to the power of 333 end exponent space plus space 1 space space and space 3 to the power of 3 to the power of 334 end exponent space plus space 1$
$27 to the power of 333 space plus space 1 to the power of 333 space space and space space space 27 to the power of 334 space plus space 1$
Now, x^m + a^m is divisible by (x + a) when m is odd
∴ 27³³³ + 1³³³ is divisible by (27 + 1) = 28
Similarly,
27³³⁴ + 1³³⁴ is never divisible by (x + a).
So, the greatest common divisor between $3 to the power of 3 to the power of 333 end exponent space plus space 1 space space and space 3 to the power of 3 to the power of 334 end exponent space plus space 1$ is 1.