Let's analyze the questions from the image and solve them step by step.

1. First Question:

• Problem: Ikkita o'zaro tub sonlarning EKUKi 108 ga teng bo'lsa, bu sonlarning ko'paytmasini toping. (If the LCM of two co-prime numbers is 108, find their product.)

Solution: If two numbers are co-prime, their Least Common Multiple (LCM or EKUK) is simply the product of the two numbers. Therefore, if their LCM is 108, their product must also be 108.

Answer: $\boxed{B) 108}$

2. Second Question:

• Problem: 45 sonining tub bo'luvchilari nechta? (How many prime divisors does 45 have?)

Solution: First, find the prime factorization of 45: $45 = 3^2 \times 5$ The prime divisors of 45 are 3 and 5, so there are 2 distinct prime divisors.

Answer: $\boxed{B) 2}$

3. Third Question:

• Problem: $Hisoblang: \frac{1^3 + 2^3 + 3^3 + 4^3}{(2 + 3)^2}$ (Calculate the given expression.)

Solution: Let's break this down: $1^3 + 2^3 + 3^3 + 4^3 = 1 + 8 + 27 + 64 = 100$ $(2 + 3)^2 = 5^2 = 25$ So, the expression becomes: $\frac{100}{25} = 4$

Answer: $\boxed{C) 4}$

4. Fourth Question:

• Problem: Given $a = 2^3 \times 3^2 \times 5$ and $b = 2^2 \times 3^3 \times 5^2$, find $\frac{EKUK(a, b)}{EKUB(a, b)}$.

Solution:

• EKUK (LCM) is found by taking the highest powers of all prime factors: $EKUK(a, b) = 2^3 \times 3^3 \times 5^2$
• EKUB (GCD) is found by taking the lowest powers of all prime factors: $EKUB(a, b) = 2^2 \times 3^2 \times 5$ Now, calculate: $\frac{EKUK(a, b)}{EKUB(a, b)} = \frac{2^3 \times 3^3 \times 5^2}{2^2 \times 3^2 \times 5} = 2^{3-2} \times 3^{3-2} \times 5^{2-1} = 2 \times 3 \times 5 = 30$

Answer: $\boxed{B) 30}$

Would you like more details on any of these solutions, or do you have other questions?

Here are 5 related questions to practice:

1. If two numbers are co-prime and their product is 72, what is their LCM?
2. What are the prime divisors of 60?
3. Calculate the sum of cubes from $1^3$ to $5^3$.
4. Given $a = 2^4 \times 3 \times 7$ and $b = 2^2 \times 3^3 \times 7^2$, find $\frac{EKUK(a, b)}{EKUB(a, b)}$.
5. If two numbers have an EKUB (GCD) of 12 and an EKUK (LCM) of 360, what is their product?

Tip: Always factorize numbers into primes when solving LCM or GCD problems.