Tag: loop

FCC Bonfire Series 132: Smallest Common Multiple

Math goodness for everyone today! We are going to be calculating the Smallest (or Least, or Lowest) Common Multiple of a range of numbers, as prompted by the Smallest Common Multiple bonfire. In mathematics, the least common multiple is the smallest positive number that is a multiple of two or more numbers (source).

As an example, take numbers 5 and 11. What is the smallest number divisible by the two? Let’s get the multiples of each and find out!

  • Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65…
  • Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99…

As you can see, the first match we come across is number 55, that number is the least common multiple. We could try and use fancy math formulas to get it, but we are going to take advantage of our dear friend, the processor to take on the workload this time (at first). Today, I shall present you three different ways to achieve the same goal. One of them will be a more readable, short version, the second will be a little messy, but takes about half the time to come up with a solution. And the third will use some clever math and come up with the answer much faster! Interested? Let’s get to it.

FCC Bonfire Series 130: Sum All Odd Fibonacci Numbers

Leonardo Fibonacci. He loves JavaScript!

Oh, good old Fibonacci! Today, we are going to be working with this marvelous integer series. For those not familiar with it, you can check what the Fibonacci sequence is here. For those interested, the guy in the picture (Leonardo Fibonacci) came up with it. He loved math and was from Pisa, Italy.

Let’s do a quick recap. The Fibonacci sequence is formed by summing the two previous numbers to obtain the next. We start off like so:

0, 1, (0 + 1), (1 + (0 + 1)), ((0 + 1) + (1 + (0 + 1))… but we can see it more clearly like so: 0, 1, 1, 2, 3, 5, 8, (8 + 5), etc.

This bonfire will have us sum all odd Fibonacci numbers up to and including the given number (if it is a Fibonacci number). For example:

// Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...

sumFibs(4) // -> 0 + 1 + 1 + 3 = 5

sumFibs(9) // -> 0 + 1 + 1 + 3 + 5 = 10

And so on. Given this information, the conclusion is obvious: we need a way to identify the three requisites for a number to be added:

  • Is Fibonacci number.
  • Is an odd number.
  • Is lower than or equal to the given number.

Let’s get to coding! We’ll start by getting the Fibonacci numbers up to the given number, once that’s out of the way, the task at hand will become trivial (we would just need to check if it’s an odd number!).