What is the least common multiple of 14 and 12?

Steps to Solve

1. Identify the multiples of each number

First, let's find the multiples of 14:

• The first few multiples are:
  • $14 \times 1 = 14$
  • $14 \times 2 = 28$
  • $14 \times 3 = 42$
  • $14 \times 4 = 56$
  • $14 \times 5 = 70$
  • $14 \times 6 = 84$
  • $14 \times 7 = 98$
  • $14 \times 8 = 112$
  • $14 \times 9 = 126$
  • $14 \times 10 = 140$

Next, let's find the multiples of 12:

• The first few multiples are:
  • $12 \times 1 = 12$
  • $12 \times 2 = 24$
  • $12 \times 3 = 36$
  • $12 \times 4 = 48$
  • $12 \times 5 = 60$
  • $12 \times 6 = 72$
  • $12 \times 7 = 84$
  • $12 \times 8 = 96$
  • $12 \times 9 = 108$
  • $12 \times 10 = 120$

2. Locate the least common multiple

Now we look for the smallest number that appears in both lists of multiples:

• The list of multiples of 14 we found includes: 14, 28, 42, 56, 70, 84, ...
• The list of multiples of 12 includes: 12, 24, 36, 48, 60, 72, 84, ...

The common multiples from both lists are:

• $84$ (it appears in both lists)
• Therefore, the least common multiple (LCM) is $84$.