Find the LCM of Denominators: 14, 15, and 3 - Step by Step

Question

Given several denominators, what is their least common multiple?

14153 \boxed{14} \boxed{15} \boxed{3}

Step-by-Step Solution

The least common multiple (LCM) of 14,15, and 314, 15, \text{ and } 3 is the smallest positive integer that is divisible by each of these numbers.

Using the prime factors, we find:

  • The prime factors of 1414 are 2 and 7.
  • The prime factors of 1515 are 3 and 5.
  • The prime factors of 33 is 3.

The LCM will be 2×3×5×7=2102 \times 3 \times 5 \times 7 = 210.

Therefore, the least common multiple is 105105.

Answer

105