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
- 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: $$ 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, \ldots $$
- 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: $$ 90, \ldots $$
- 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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