$\frac{3}{m-1}+m+n$
L.C.M =
Answer (1)
Identify the denominators in the expression: m − 1 , 1 , and 1 .
Find the Least Common Multiple (LCM) of the denominators.
Since one of the denominators is 1, the LCM is simply the other denominator, m − 1 .
The LCM of the denominators in the expression is m − 1 .
Explanation
Understanding the Problem The problem asks us to find the Least Common Multiple (LCM) of the denominators in the expression m − 1 3 + m + n .
Identifying the Denominators Let's identify the denominators in the given expression. We have the fraction m − 1 3 , which has a denominator of m − 1 . The other terms, m and n , can be written as 1 m and 1 n , respectively. So, their denominators are both 1.
Finding the LCM Now, we need to find the LCM of the denominators m − 1 , 1 , and 1 . The LCM is the smallest expression that is a multiple of all the denominators. Since 1 is a factor of every expression, we only need to consider m − 1 . Therefore, the LCM of m − 1 , 1 , and 1 is simply m − 1 .
Final Answer Thus, the Least Common Multiple (LCM) of the denominators in the expression m − 1 3 + m + n is m − 1 .
Examples
Understanding LCM is crucial when combining fractions with different denominators, such as in cooking or construction. For instance, if you're adjusting a recipe that calls for 2 1 cup of flour and 3 1 cup of sugar, you need to find a common denominator (LCM of 2 and 3, which is 6) to accurately combine the ingredients. This ensures the proportions remain correct, and the dish turns out as expected. Similarly, in construction, when mixing different ratios of materials like cement and sand, finding the LCM helps maintain the structural integrity of the mixture.
