Find three pairs of numbers for which the LCM (least common multiple) is the product of the two numbers;

The pairs and LCMs are:
8 and 12: 24; 3 and 15: 15; 7 and 11: 77; 9 and 10: 90; 24 and 36: 72; 20 and 25: 100; 14 and 42: 42; 30 and 12: 60

The LCM is the product if they have no factors in common (relatively prime)

Now it should be easy to pick the proper pairs.

In fact, since they actually gave you the LCM's, it's just a matter of seeing whether the two numbers multiply to give the indicated LCM!

To find three pairs of numbers for which the least common multiple (LCM) is the product of the two numbers, we can use the following approach:

1. Choose a pair of numbers (a, b) and calculate their LCM.
2. If the LCM is equal to the product of a and b, then this pair satisfies the condition.
3. Repeat steps 1 and 2 to find additional pairs.

Let's go through the given pairs and calculate their LCM to verify if the LCM is indeed the product of the two numbers:

1. Pair (8, 12):
- LCM(8, 12) = 24.
- 8 * 12 = 96 ≠ 24.
- The LCM is not equal to the product of the two numbers.

2. Pair (3, 15):
- LCM(3, 15) = 15.
- 3 * 15 = 45 ≠ 15.
- The LCM is not equal to the product of the two numbers.

3. Pair (7, 11):
- LCM(7, 11) = 77.
- 7 * 11 = 77.
- The LCM is equal to the product of the two numbers.

Therefore, the pair (7, 11) satisfies the condition.

4. Pair (9, 10):
- LCM(9, 10) = 90.
- 9 * 10 = 90.
- The LCM is equal to the product of the two numbers.

Therefore, the pair (9, 10) satisfies the condition.

5. Pair (24, 36):
- LCM(24, 36) = 72.
- 24 * 36 = 864 ≠ 72.
- The LCM is not equal to the product of the two numbers.

6. Pair (20, 25):
- LCM(20, 25) = 100.
- 20 * 25 = 500 ≠ 100.
- The LCM is not equal to the product of the two numbers.

7. Pair (14, 42):
- LCM(14, 42) = 42.
- 14 * 42 = 588 ≠ 42.
- The LCM is not equal to the product of the two numbers.

8. Pair (30, 12):
- LCM(30, 12) = 60.
- 30 * 12 = 360 ≠ 60.
- The LCM is not equal to the product of the two numbers.

Therefore, out of the given pairs, only two pairs (7, 11) and (9, 10) have the LCM equal to the product of the two numbers.