“So, the least common multiple of $52$ and $64$,” said the Mathematical Ninja, “is $13 \times 16 \times 4$, which is $832$.”

“H-how did you do that?!” asked the student.

The student was clearly new around here, so the Mathematical Ninja went easy on him. “Very simple,” he said. “I rearranged the order to make it $13 \times 4 \times 16$, or $52 \times 16$.”

He thought for a moment, and nodded. “But how did you do that?”

“Very simple,” said the Mathematical Ninja. “$16 = 2 \times 8$, so I can make it $52 \times 2 \times 8$, or $104 \times 8$, which is $800 + 32$.”

The student’s eyes opened. “You can… shuttle numbers like that?”

The Mathematical Ninja nodded, gravely. “You’ve done standard form, right?”

A nod.

“Say you’ve worked something out to be $25 \times 10^4$. Obviously the $25$ is too big - but you can split it up as $2.5 \times 10 \times 10^4$ or $2.5 \times 10^5$.”

In that moment, the student became enlightened.