Playing Till The Bridge

The guitar and bass comes in together, thus the bar where the two finish together would be:

As the keyboard starts 3 bars after this, all we need to do is to find a common multiple of 6 and 16, minus three, and check if it's a multiple of 5.

L.C.M. of 6 and 16 is $2\times3\times8 = 48$

48 luckily for us, when 3 is subtracted from it, is 45. Therefore the answer is 48.

(I wonder how crazy their music would sound)

The guitar and the bass start together. All the instruments must end at the same measure. Hence, for now, we'll consider only the guitar and the bass.

They can be at sync only on the first number that is divisible by both $16$ and $6$ . That is just $\text{lcm}(16,6) = 48$ .

Now we need to find the first number $x$ such that $x \geq 48$ and $(x - 3)\mod{5} = 0$ and $x$ should be divisible by both $6$ and $16$ . (Because the keyboard started $3$ measures late). This happens to be easy, it is $48$ as $48 - 3 = 45$ is divisible by $5$ .

Hence, our answer is $\boxed{48}$

The guitar and bass will end together at measure 48 (the LCM of 16 and 6). The keyboard part is 5 measures long. 5 $\times$ 9 is 45, which is 3 less than 48. Therefore the parts will end together at the end of measure 48.

step 1 : take the L.C.M of 6 and 16 = 48 => the bridge of guitar a d bass step 2 : since keyboard comes after 3 measure delay, 48-3=45. which is a multiple of 5. hence the bridge occurs at 48th measure