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Mathematics

Grade5

Easy

Question

The number that could NOT be a common denominator for these three fractions is?
$1 third$ and $2 over 5$ and $3 over 10$ .

15
30
60
90

hint Hint:

The number which cannot be divided by Least Common denominator will be the answer of this question. We have to find the least common denominator and for that we have to find the least common multiple of denominators. Least Common Denominator (LCD) is the least common multiple of denominator of a set of fractions. The method of calculating the LCD is same as calculation of Least Common Multiple of fractions denominators. The least common multiple

The correct answer is: 15

The least common denominator is the lowest common multiple of the denominators of a set of fractions.
Step1: We are given fractions $1 third$ and $2 over 5$ and $3 over 10$ .
And we have to find the LCM of denominators of the fractions i.e., $3 comma 5 comma 10$
Step2: We know that Multiples of $3$ are: $3 comma 6 comma 9 comma 12 comma 15 comma 18 comma 21 comma 24 comma 27 comma 30 comma 33 space horizontal ellipsis$
And the multiples of $5$ are: $5 comma 10 comma 15 comma 20 comma 25 comma 30 space horizontal ellipsis$
And the multiples of $10$ are: $10 comma space 20 comma space 30 comma space 40 comma 50 comma 60 space horizontal ellipsis$
Step3: Now we have to find the LCM of $3 comma 5 space$ and $10$ .
From the above multiples of $3 comma 5 space$ and $10$ . it can be easily seen that the least common multiple of is $30$
Hence the least common denominator of $3 comma 5 space$ and $10$ is $30$ .
So any number which is not a multiple of $30$ will be the answer of this question and from options it can be easily seen that $15$ is not divisible by $30$
Multiples of 3 are 3, 6, 9, 12, …
Multiples of 5 are 5, 10, 15, 20, …
Multiples of 10 are 10, 20, 30, 40, …
15 is not divisible by the denominator 10.

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