LCM of 14 and 21

Find the Least Common Multiple (LCM) of 14 and 21. The LCM is the smallest number that both 14 and 21 divide evenly.

Answer: LCM(14, 21) = 42

Step-by-Step Solution

Step 1 List the Multiples of 14

To find the LCM of 14 and 21, we first list the multiples of each number.

Multiples of 14 are: 14 × 1, 14 × 2, 14 × 3, ...

Multiples of 14: 14, 28, 42, 56, 70, ...

Step 2 List the Multiples of 21

Now we list the multiples of 21:

Multiples of 21: 21, 42, 63, 84, ...

Step 3 Find the Least Common Multiple

The common multiples are numbers that appear in both lists.

The smallest common multiple is the LCM.

Looking at both lists, the first number that appears in both is 42.

LCM(14, 21) = 42

Step 4 Prime Factorization Method

We can also find the LCM using prime factorization:

14 = 2 × 7

21 = 3 × 7

Take each prime factor with the highest power:

LCM = 2 × 3 × 7 = 42

Step 5 Using the GCF Formula

The LCM can be calculated using the GCF with this formula:

LCM(a, b) = (a × b) ÷ GCF(a, b)

GCF(14, 21) = 7

LCM = (14 × 21) ÷ 7 = 294 ÷ 7 = 42

Step 6 Final Answer

LCM(14, 21) = 42