Project Euler: Problem 5

Problem 5

Hand-written solution

This is a least common multiples problem. There is a straightforward formula for this that involves multiplying the highest power of each prime number $<= N$. In this case, $N=20$.

It's easier to do this one by hand than to write the code.

For example (skipping "$1$" for obvious reasons):

$N=2; \quad 2^{1}=2$
$N=3; \quad 2^{1} \times 3^{1}=6$
$N=4; \quad 2^{2} \times 3^{1}=12$
$N=5; \quad 2^{2} \times 3^{1} \times 5^{1} = 60$
$N=6; \quad 2^{2} \times 3^{1} \times 5^{1} = 60$
$N=7; \quad 2^{2} \times 3^{1} \times 5^{1} \times 7^{1} = 420$
$N=8; \quad 2^{3} \times 3^{1} \times 5^{1} \times 7^{1} = 840$
$N=9; \quad 2^{3} \times 3^{2} \times 5^{1} \times 7^{1} = 2520$
$\quad \vdots$
$N=20; \quad 2^{4} \times 3^{2} \times 5^{1} \times 7^{1} \times 11^{1} \times 13^{1} \times 17^{1} \times 19^{1} = 232,792,560$

Conclusion

A fairly straightforward problem that didn't need coding for a change.

Final answer

$232,792,560$