Final answer:
To find the least common multiple of 12, 4, and 10, list the prime factors of each number, take the highest powers of those primes represented, and multiply them together, which results in the LCM of 60.
Step-by-step explanation:
The least common multiple (LCM) of the numbers 12, 4, and 10 is found by first listing the prime factors of each number. For 12, the prime factors are 2² × 3; for 4, the prime factors are 2²; and for 10, the prime factors are 2 × 5.
To find the LCM, we take the highest powers of all prime factors present in any of the numbers: 2² (as 2³ is not required), 3, and 5.
Multiplying these together gives us the LCM: 2² × 3 × 5, which calculates to 4 × 3 × 5 = 60.
Therefore, the LCM of 12, 4, and 10 is 60.