Find the least common denominator for these fractions. Enter your answer in the space provided.
$\frac{2}{3}$ and $\frac{2}{7}$
Answer (2)
Identify the denominators: The denominators of the fractions are 3 and 7.
Find the least common multiple (LCM): Since 3 and 7 are prime numbers, their LCM is their product.
Calculate the product: 3 × 7 = 21 .
The least common denominator (LCD) is 21 .
Explanation
Understanding the Problem We are asked to find the least common denominator (LCD) of two fractions: 3 2 and 7 2 . The least common denominator is the smallest multiple that the denominators of both fractions share. In this case, the denominators are 3 and 7.
Finding the Least Common Multiple (LCM) To find the LCD, we need to find the least common multiple (LCM) of the denominators 3 and 7. Since 3 and 7 are both prime numbers, they do not share any common factors other than 1.
Calculating the LCM When the numbers are prime, the LCM is simply the product of the numbers. So, we multiply 3 and 7 to find the LCM.
The Result The calculation is: 3 × 7 = 21 . Therefore, the least common multiple of 3 and 7 is 21.
Final Answer The least common denominator (LCD) of the fractions 3 2 and 7 2 is 21.
Examples
Imagine you're baking a cake and need to measure ingredients using fractions. If one recipe calls for 3 2 of a cup of flour and another calls for 7 2 of a cup of sugar, using the least common denominator (LCD) helps you find a common unit to easily compare and combine these measurements. In this case, the LCD of 3 and 7 is 21, so you can think of the flour as 21 14 of a cup and the sugar as 21 6 of a cup, making it simpler to manage your ingredients.
The least common denominator (LCD) of the fractions 3 2 and 7 2 is 21. This is found by calculating the least common multiple (LCM) of the denominators, which in this case is simply their product since both are prime. Thus, 3 × 7 = 21 .
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