lcm of 18 and 7

Steps to Solve

1. List the multiples of each number

Start by listing the multiples of 18 and 7.

Multiples of 18:

• $18 \times 1 = 18$
• $18 \times 2 = 36$
• $18 \times 3 = 54$
• $18 \times 4 = 72$
• $18 \times 5 = 90$
• $18 \times 6 = 108$
• $18 \times 7 = 126$
• $18 \times 8 = 144$
• $18 \times 9 = 162$
• $18 \times 10 = 180$

Multiples of 7:

• $7 \times 1 = 7$
• $7 \times 2 = 14$
• $7 \times 3 = 21$
• $7 \times 4 = 28$
• $7 \times 5 = 35$
• $7 \times 6 = 42$
• $7 \times 7 = 49$
• $7 \times 8 = 56$
• $7 \times 9 = 63$
• $7 \times 10 = 70$

2. Identify the common multiples

Now, look for common multiples in both lists.

From our lists: Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70

There are no common multiples in the lower range.

3. Calculate the LCM using the formula

We can use the formula for LCM based on the relationship between the product of the numbers and their GCD (Greatest Common Divisor):

$$ LCM(a, b) = \frac{a \times b}{GCD(a, b)} $$

For the numbers 18 and 7:

• The GCD of 18 and 7 is 1 (since they are coprime).

Now we can plug the numbers into the formula:

$$ LCM(18, 7) = \frac{18 \times 7}{1} = 126 $$

4. State the final answer

The least common multiple of 18 and 7 is 126.