Highest common factor (HCF) and lowest common multiple (LCM)
a)(i) List all the factors of 90. There are 12 in total.
(ii) List all the factors of 105. There are 8 in total.
*List the numbers in ascending order separated by commas.
b) What is the Highest Common Factor of 90 and 105?
a)(i)
a)(ii)
b)
Lowest Common Multiple
a)(i) List the first eight multiples of 90.
(ii) List the first eight multiples of 105.
*List the numbers in ascending order separated by commas.
b) What is the Lowest Common Multiple of 90 and 105?
a)(i)
a)(ii)
b)
Can we find the HCF and LCM of numbers from their prime factorizations?
The prime factorization of $90=2\times$
$\times$
The prime factorization of $105=3\times$
$\times$
$90=2\times \textcolor{red}{3} \times 3 \times \textcolor{red}{5}$
$105=\textcolor{red}{3} \times \textcolor{red}{5} \times 7$
The HCF of $90$ and $105$ is $\textcolor{red}{3} \times \textcolor{red}{5} =$
.
$90=2\times \textcolor{red}{3} \times 3 \times \textcolor{red}{5}$
$105=\textcolor{red}{3} \times \textcolor{red}{5} \times 7$
The LCM of $90$ and $105$ is $2 \times \textcolor{red}{3} \times 3 \times \textcolor{red}{5} \times 7=$
.
The prime factorization of $2772=2$$\times3$$\times$
$\times 11$
The prime factorization of $9450=2\times3$$\times5$$\times 7$
$2772=\textcolor{red}{2} \times 2 \times \textcolor{red}{3} \times \textcolor{red}{3} \times \textcolor{red}{7} \times 11$
$9450=\textcolor{red}{2} \times \textcolor{red}{3} \times \textcolor{red}{3} \times 3 \times 5 \times 5 \times \textcolor{red}{7}$
The HCF of $2772$ and $9450$ is
.
$2772=\textcolor{red}{2} \times 2 \times \textcolor{red}{3} \times \textcolor{red}{3} \times \textcolor{red}{7} \times 11$
$9450=\textcolor{red}{2} \times \textcolor{red}{3} \times \textcolor{red}{3} \times 3 \times 5 \times 5 \times \textcolor{red}{7}$
The LCM of $2772$ and $9450$ is
.