LCM of 20 and 36

Steps to Solve

1. Find the Prime Factorization of Each Number

First, we need to factor both numbers into their prime factors.

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

For 36:
$$ 36 = 2^2 \times 3^2 $$

2. Identify the Highest Powers of Each Prime Factor

Next, we take each unique prime factor from the factorizations and find the highest power for each.

• For the prime factor 2, the highest power is $2^2$.
• For the prime factor 3, the highest power is $3^2$.
• For the prime factor 5, the highest power is $5^1$.

3. Multiply the Highest Powers Together

Now we multiply all the highest powers we identified:

$$ LCM(20, 36) = 2^2 \times 3^2 \times 5^1 $$

Calculating this gives:

$$ 2^2 = 4, \quad 3^2 = 9, \quad 5^1 = 5 $$

So:

$$ LCM(20, 36) = 4 \times 9 \times 5 $$

4. Calculate the Final Product

Now we will perform the multiplication step-by-step:

First, multiply $4$ and $9$:

$$ 4 \times 9 = 36 $$

Then multiply the result by $5$:

$$ 36 \times 5 = 180 $$

So, the least common multiple of 20 and 36 is 180.