Question

I am the square of the number that is 68 less than the product of the LCM of 2 and 3 and the LCM of 3 and 4. What number am I ?

Answer 1

Let the number be $x$

Given that square of the number is 68 less than the product of the LCM of 2 and 3 and the LCM of 3 and 4.

Therefore, $x^2+68=\left(LCM\right(2,3\left)\right)\times \left(LCM\right(3,4\left)\right)$

$⟹x^2+68=(2\times 3)\times (3\times 4)$

$⟹x^2+68=72$

$⟹x^2=72-68$

$⟹x^2=4$

$⟹x=2$

Therefore the number is $2$