# LCM of 2 and 5

#### Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 2 and 5. To find the LCM, we will identify the smallest number that is a multiple of both 2 and 5.

10

The least common multiple (LCM) of 2 and 5 is 10

#### Steps to Solve

1. List the prime factors of each number

Identify the prime factors of each number:

• For 2, the prime factor is 2.
• For 5, the prime factor is 5.
1. Determine the highest power of each prime factor

The next step is to take the highest power of each prime factor appearing in the factorization of 2 and 5.

• Highest power of 2: $2^1$
• Highest power of 5: $5^1$
1. Multiply these highest powers together

Now multiply these highest powers together to get the LCM:

$$ext{LCM}(2, 5) = 2^1 \times 5^1 = 10$$

The least common multiple (LCM) of 2 and 5 is 10

The LCM is useful in problems involving adding, subtracting, or comparing fractions with different denominators. Fun fact: the LCM of any two prime numbers will always be their product!

#### Tips

A common mistake is to confuse the LCM with the greatest common divisor (GCD). Remember, the LCM of two numbers is the smallest number that both original numbers can divide into without leaving a remainder.

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