Question

What is the LCD of the fractions \[\dfrac{1}{3}\] and\[\dfrac{{11}}{{15}}\]?

Answer 1

Hint: In this question, we have to find out the least common denominator of the given fractions.
For finding that we have to find the lowest common multiple of the two denominators. First, we need to do prime factorization and then multiplying all the primes taking the common terms only once. After that, we will get the common denominator.

Complete step by step answer:
We need to find out the least common denominator of the fractions\[\dfrac{1}{3}\] and\[\dfrac{{11}}{{15}}\].
We have to find out the lowest common multiple of the two denominators.
First, we need to do prime factorization for the two numbers\[3and15\].
We get,
\[3 = 1 \times 3\].
\[15 = 3 \times 5\].
Now the common prime number is\[3\], for finding the L.C.M we will multiply the common term once and the other terms.
Thus the L.C.M of\[3and15\]=\[3 \times 5 = 15\]
Now we can convert the fractions like the following way:
\[\dfrac{1}{3} \times 1\]and \[\dfrac{{11}}{{15}} \times 1\]
Or,\[\dfrac{1}{3} \times \dfrac{5}{5}\]and \[\dfrac{{11}}{{15}} \times 1\]
i.e., \[\dfrac{5}{{15}}\] and \[\dfrac{{11}}{{15}}\]
Hence, \[15\] is the least common denominator or L.C.D. of the fractions\[\dfrac{1}{3}\] and\[\dfrac{{11}}{{15}}\].

Note:
Proper fraction:
A fraction where the numerator (the top number) is less than the denominator (the bottom number). For example,\[\dfrac{1}{4},\dfrac{3}{5}\] etc.
Improper fraction:
A fraction where the numerator (the top number) is greater than the denominator (the bottom number).
For example,\[\dfrac{7}{5},\dfrac{3}{2}\] etc.
Mixed fraction:
A whole number and a proper fraction are combined into one “Mixed fraction”.
For example,\[5\dfrac{1}{2},7\dfrac{1}{5}\] etc.
L.C.D.:
In mathematics, the lowest common denominator or least common denominator is the lowest common multiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions.