What is the lowest common multiple of 14 and 15?

Understand the Problem

The question is asking for the lowest common multiple (LCM) of the numbers 14 and 15. To solve this, we will look for the smallest number that is a multiple of both 14 and 15.

Answer

The lowest common multiple (LCM) of 14 and 15 is $210$.

Steps to Solve

Identify the prime factors of each number

First, we need to find the prime factorization of the numbers 14 and 15.

For 14: $$ 14 = 2 \times 7 $$

For 15: $$ 15 = 3 \times 5 $$

List out the highest powers of each prime factor

Next, we need to identify all the unique prime factors from both numbers and take the highest power of each.

From 14, we have:
- $2^1$
- $7^1$
From 15, we have:
- $3^1$
- $5^1$

Calculate the LCM using the prime factors

Now, we multiply all the highest powers of the prime factors together to find the LCM.

$$ LCM = 2^1 \times 3^1 \times 5^1 \times 7^1 $$

Perform the multiplication

Now calculate the product step-by-step:

First, multiply: $$ 2 \times 3 = 6 $$

Then: $$ 6 \times 5 = 30 $$

Finally: $$ 30 \times 7 = 210 $$

So, the lowest common multiple of 14 and 15 is 210.

The lowest common multiple (LCM) of 14 and 15 is 210.

More Information

The LCM is the smallest number that both 14 and 15 divide evenly into. This concept is useful in various applications, especially in adding fractions with different denominators or solving problems where common multiples are needed.

Tips

Forgetting to consider all prime factors of both numbers. Ensure you check all prime factors when calculating LCM.
Not multiplying all prime factors together correctly. Keep track of each multiplication step to avoid mistakes.

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