Answer :
We start by considering the division of 360 sweets in the ratio
$$5:3:4.$$
**Step 1: Determining the Smallest Share**
1. First, compute the total number of parts:
$$5 + 3 + 4 = 12.$$
2. Each part thus represents:
$$\frac{360}{12} = 30 \text{ sweets}.$$
3. The smallest share corresponds to the smallest number in the ratio, which is $3$. Therefore, the smallest share is:
$$3 \times 30 = 90 \text{ sweets}.$$
**Step 2: Simplifying the Ratio $12:36:60$ to its Lowest Terms**
1. Find the greatest common divisor (GCD) of $12$, $36$, and $60$. The GCD is $12$.
2. Divide each term of the ratio by $12$:
\[
\begin{aligned}
12 \div 12 &= 1, \\
36 \div 12 &= 3, \\
60 \div 12 &= 5.
\end{aligned}
\]
3. Thus, the simplified ratio is:
$$1:3:5.$$
**Final Answer:**
- The smallest share is $\boxed{90}$ sweets.
- The ratio $12:36:60$ in its lowest terms is $\boxed{1:3:5}$.
$$5:3:4.$$
**Step 1: Determining the Smallest Share**
1. First, compute the total number of parts:
$$5 + 3 + 4 = 12.$$
2. Each part thus represents:
$$\frac{360}{12} = 30 \text{ sweets}.$$
3. The smallest share corresponds to the smallest number in the ratio, which is $3$. Therefore, the smallest share is:
$$3 \times 30 = 90 \text{ sweets}.$$
**Step 2: Simplifying the Ratio $12:36:60$ to its Lowest Terms**
1. Find the greatest common divisor (GCD) of $12$, $36$, and $60$. The GCD is $12$.
2. Divide each term of the ratio by $12$:
\[
\begin{aligned}
12 \div 12 &= 1, \\
36 \div 12 &= 3, \\
60 \div 12 &= 5.
\end{aligned}
\]
3. Thus, the simplified ratio is:
$$1:3:5.$$
**Final Answer:**
- The smallest share is $\boxed{90}$ sweets.
- The ratio $12:36:60$ in its lowest terms is $\boxed{1:3:5}$.
