Final answer:
The LCM for each pair of numbers is found by identifying the smallest multiple common to both numbers or by using prime factorization with the highest powers of all prime factors. The LCMs for the pairs (8,12), (6,7), (3,4), and (4,9) are 24, 42, 12, and 36, respectively.
Step-by-step explanation:
To find the Least Common Multiple (LCM) of each pair of numbers, you can list the multiples of each number and then identify the smallest multiple that appears on both lists.
Alternatively, you can use the method of prime factorization for each number, multiplying together the highest powers of all prime factors.
Pair 1: 8 and 12
Prime factorization of 8 is 23, and for 12, it is 22 × 3. The LCM is 23 × 3 = 24.
Pair 2: 6 and 7
Since 6 and 7 are coprime (no common factors other than 1), the LCM is just 6 × 7 = 42.
Pair 3: 3 and 4
The LCM of 3 (31) and 4 (22) is 3 × 22 = 12.
Pair 4: 4 and 9
Prime factorization of 4 is 22, and for 9, it is 32. The LCM is 22 × 32 = 36.