It looks like you uploaded an image showing a math quiz. The task is to find the Least Common Multiple (LCM) for several pairs or groups of numbers. Here is the list of the problems shown:

1. LCM of $24$ and $60$
2. LCM of $5$, $18$, and $20$
3. LCM of $6$, $18$, and $24$
4. LCM of $15$, $20$, and $30$
5. LCM of $12$, $36$, and $48$

Let me solve each of these problems one by one:

1. LCM of $24$ and $60$

The prime factorizations are:

• $24 = 2^3 \times 3$
• $60 = 2^2 \times 3 \times 5$

To find the LCM, take the highest powers of all primes involved:

• $2^3$, $3$, and $5$.

LCM $= 2^3 \times 3 \times 5 = 120$.

2. LCM of $5$, $18$, and $20$

Prime factorizations are:

• $5 = 5$
• $18 = 2 \times 3^2$
• $20 = 2^2 \times 5$

LCM takes the highest powers:

• $2^2$, $3^2$, and $5$.

LCM $= 2^2 \times 3^2 \times 5 = 180$.

3. LCM of $6$, $18$, and $24$

Prime factorizations are:

• $6 = 2 \times 3$
• $18 = 2 \times 3^2$
• $24 = 2^3 \times 3$

LCM takes the highest powers:

• $2^3$ and $3^2$.

LCM $= 2^3 \times 3^2 = 72$.

4. LCM of $15$, $20$, and $30$

Prime factorizations are:

• $15 = 3 \times 5$
• $20 = 2^2 \times 5$
• $30 = 2 \times 3 \times 5$

LCM takes the highest powers:

• $2^2$, $3$, and $5$.

LCM $= 2^2 \times 3 \times 5 = 60$.

5. LCM of $12$, $36$, and $48$

Prime factorizations are:

• $12 = 2^2 \times 3$
• $36 = 2^2 \times 3^2$
• $48 = 2^4 \times 3$

LCM takes the highest powers:

• $2^4$ and $3^2$.

LCM $= 2^4 \times 3^2 = 144$.

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Summary of LCMs:

1. LCM of $24$ and $60$ = 120
2. LCM of $5$, $18$, and $20$ = 180
3. LCM of $6$, $18$, and $24$ = 72
4. LCM of $15$, $20$, and $30$ = 60
5. LCM of $12$, $36$, and $48$ = 144

Let me know if you want further details or if you have any other questions.

Here are 5 related questions for more practice:

1. What is the LCM of 10, 15, and 25?
2. How do you find the LCM of numbers using their prime factorizations?
3. What is the GCD (Greatest Common Divisor) of 18, 24, and 30?
4. Can the LCM of two numbers ever be smaller than both numbers? Why or why not?
5. How does finding the LCM help in solving fraction addition problems?

Tip: The LCM is useful for adding and subtracting fractions with different denominators!