Find the least number by which $1,200$ must be multiplied to make it a perfect square.

First, find the prime factorization of $1,200$:
$$1,200=12\times 100$$

$$1,200=(2^2\times 3)\times (2^2\times 5^2)$$

$$1,200=2^4\times 3^1\times 5^2$$

To make it a perfect square, the powers of all prime factors must be even numbers.
Here, the power of $3$ is $1$ (odd). Thus, it needs to be multiplied by $3$ to make the power even ($3^2$).

Therefore, the least number by which $1,200$ must be multiplied is $3$.