What is the least common multiple of 28 and 20?

Steps to Solve

1. Find the prime factorization of each number

To find the LCM, we need to break down each number into its prime factors.

For 28: $$ 28 = 2^2 \times 7^1 $$

For 20: $$ 20 = 2^2 \times 5^1 $$

2. Identify the highest power of each prime factor

Next, we will take each unique prime factor from both factorizations and determine the highest exponent used.

• For the prime factor 2: the highest power is $2^2$ (from both 28 and 20).
• For the prime factor 5: the highest power is $5^1$ (from 20).
• For the prime factor 7: the highest power is $7^1$ (from 28).

3. Calculate the LCM using the highest powers

Now we multiply these highest powers together to find the LCM.

$$ LCM = 2^2 \times 5^1 \times 7^1 $$

Calculating this gives:

$$ LCM = 4 \times 5 \times 7 $$

4. Final multiplication

Now we perform the multiplication step-by-step:

First, calculate $4 \times 5$: $$ 4 \times 5 = 20 $$

Then, multiply the result by 7: $$ 20 \times 7 = 140 $$

Thus, the least common multiple of 28 and 20 is 140.