Factors & Multiples Practice 1
This section features six targeted practice questions designed to strengthen your skills in finding the HCF and LCM of numbers using the selection method. These questions are carefully chosen based on the most commonly tested problem types in exams. By mastering these six question types, students greatly increase their chances of successfully tackling similar problems in the actual exam.
Related Lessons:
Practice 1 - Question 1
The numbers 392 and 588, written as the products of their prime factors, are
\[
\begin{align*}
392&=2^3\times7^2\\
588&=2^2\times3\times7^2\\
\end{align*}
\]
Find the lowest common multiple of 392 and 588.
Solution:
To find the LCM, we select all the prime factors, and select the highest.
\[
\begin{align*}
392&=2^3\times7^2\\
588&=2^2\times3\times7^2\\
LCM&=2^3\times3\times7^2=1176\\
\end{align*}
\]
Practice 1 - Question 2
By expressing 3450 as a product of its prime factors, find the smallest integer value of k such that 3450k is a perfect square.
Solution:
\[
\begin{align*}
3450&=2\times3\times5^2\times23\\
3450k&=2^2\times3^2\times5^2\times{23}^2\\
k&=\frac{2^2\times3^2\times5^2\times{23}^2}{2\times3\times5^2\times23}\\
&=2\times3\times23\\
&=138\\
\end{align*}
\]
Practice 1 - Question 3
The number 945 and 11025, written as the products of its prime factors is \(945=3^3\times5\times7 \) and \(11025=3^2\times5^2\times7^2\) respectively. Find the smallest positive integer value of n for which 945n is a multiple of 11025.
Solution:
\[
\begin{align*}
\frac{945n}{11025}&=\frac{3^3\times5\times7\times n}{3^2\times5^2\times7^2}\\
&=\frac{3\times n}{5\times7}\\
\end{align*}
\]
Therefore, \(n=5\times7=35\)
Practice 1 - Question 4
Keith, Faith and Nicole each visit the library once every 3 days. 5 days and 12 days respectively. If they meet at the library today, how many days later will they meet again?
Solution:
Now, since we are expecting the answer to be larger than 12 days, we will find the LCM.
\[
\begin{align*}
3&=3\\
5&=5\\
12&=2^2\times3\\
LCM&=2^2\times3\times5\\
&=60\\
\end{align*}
\]
Practice 1 - Question 5
Cindy bought 48 apples, 72 oranges and 96 pears. If she wants each type of fruit to be distributed equally among a certain number of fruit baskets, what is the greatest number of fruit baskets that can be prepared?
Solution:
Now, since we are dividing up the apples, oranges and pears, it must be smaller than 48 apples, so we will find the HCF.
\[
\begin{align*}
48&=2^4\times3\\
72&=2^3\times3^2\\
96&=2^5\times3\\
HCF&=2^3\times3\\
&=24\\
\end{align*}
\]
Practice 1 - Question 6
Find two numbers if their Lowest Common Multiple is 100 and their Highest Common Factor is 5. Give two possible pairs of answers.
Solution:
\[
\begin{align*}
Product\ &=\ HCF\ \times\ LCM\\
&=5\times100\\
&=5\times2^2\times5^2\\
&=2^2\times5^3\\
\end{align*}
\]
By performing selection by breaking up the index numbers, first pair is 25 and 20. Second pair is 100 and 5
Watch Full Solution Step-By-Step
To better understand how to solve the questions above, it is helpful to learn the solutions step by step. The video below demonstrates clearly how each solution is developed.