least common multiple of 21 and 49

Steps to Solve

1. List the multiples of each number

First, we will find the multiples of both numbers.

For 21, the first few multiples are: $$ 21, 42, 63, 84, 105, ... $$

For 49, the first few multiples are: $$ 49, 98, 147, 196, 245, ... $$

2. Identify the common multiples

Next, we look for multiples that appear in both lists.

The multiples we found are:

• 21: $21, 42, 63, 84, 105, ...$
• 49: $49, 98, 147, 196, 245, ...$

The smallest multiple that is common to both lists is not immediately visible, so we will need to use another method.

3. Use the prime factorization method

Now, let's find the prime factorization of both numbers.

For 21: $$ 21 = 3 \times 7 $$

For 49: $$ 49 = 7^2 $$

4. Calculate the LCM using the highest power of each prime factor

To find the LCM, we take the highest power of each prime factor:

• From 21: $3^1$ and $7^1$
• From 49: $7^2$

Now, we calculate the LCM: $$ LCM = 3^1 \times 7^2 = 3 \times 49 = 147 $$

Thus, the least common multiple of 21 and 49 is 147.