Certainly! Let's solve this step by step.
1. Understanding the problem: We are given the Least Common Multiple (LCM) of two numbers which are co-prime and one of those numbers. We need to find the other number.
2. Definition of co-prime numbers: Co-prime numbers are pairs of numbers that have no common factors other than 1. For example, 8 and 15 are co-prime.
3. Property of LCM for co-prime numbers: If two numbers are co-prime, their LCM is simply the product of the two numbers. This is because co-prime numbers share no common factors, so the least common multiple is just the multiplication of the two numbers.
4. Given values:
- The LCM of the two numbers is 153.
- One of the numbers is 17.
5. Finding the other number:
- Let the other number be denoted as [tex]\( N \)[/tex].
- According to the property, if two numbers are co-prime and their LCM is given, then their product equals the LCM.
- Therefore,
[tex]\[
\text{LCM}(17, N) = 17 \times N = 153
\][/tex]
6. Solving for [tex]\( N \)[/tex]:
- Rearrange the equation to solve for [tex]\( N \)[/tex]:
[tex]\[
N = \frac{153}{17}
\][/tex]
7. Perform the division:
- Calculate [tex]\( \frac{153}{17} \)[/tex]:
[tex]\[
\frac{153}{17} = 9
\][/tex]
Thus, the other number is [tex]\( 9 \)[/tex].
