Final answer:
The least common multiple (LCM) of 75 and 15 is 75, which is option a). Since 75 is already a multiple of 15, it is the smallest number that is a multiple of both.
Step-by-step explanation:
Least Common Multiple of 75 and 15
The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. In this case, we need to find the LCM of 75 and 15. Since 75 is already a multiple of 15 (75 = 5 × 15), the LCM is directly the larger number, which is 75.
Therefore, option a) 75 is the least common multiple of 75 and 15. There's no need to go to higher multiples like 150, 225, or 300 because 75 is the smallest number that both 75 and 15 divide into without a remainder.