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lcm of 18 and 5

Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 18 and 5, which involves finding the smallest positive integer that is a multiple of both numbers.

Answer

The least common multiple (LCM) of 18 and 5 is $90$.
Answer for screen readers

The least common multiple (LCM) of 18 and 5 is $90$.

Steps to Solve

  1. List the multiples of each number

Start by listing out the multiples of both 18 and 5.

For 18, the first few multiples are: $$ 18, 36, 54, 72, 90, 108, \ldots $$

For 5, the first few multiples are: $$ 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, \ldots $$

  1. Find the common multiples

Next, identify the common multiples from the lists.

Looking at our lists:

  • The multiples of 18 are: $$ 18, 36, 54, 72, 90, \ldots $$
  • The multiples of 5 are: $$ 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, \ldots $$

The common multiples are: $$ 90, \ldots $$

  1. Identify the least common multiple (LCM)

The least common multiple is the smallest number that appears in both lists.

From our common multiples:

  • The smallest is $$ 90 $$.

So, the LCM of 18 and 5 is $$ 90 $$.

The least common multiple (LCM) of 18 and 5 is $90$.

More Information

The least common multiple is often used in problems involving fractions, where you might need to find a common denominator. Knowing how to find the LCM can help simplify many mathematical problems.

Tips

  • A common mistake is to confuse the least common multiple with the greatest common divisor (GCD). Remember that LCM is about finding the smallest number that is a multiple of both, while GCD finds the largest number that divides both without leaving a remainder.
  • Sometimes, people skip listing enough multiples, so it's important to list several multiples to ensure you find the least one.
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