Question

Find the HCF and LCM of the following pairs of numbers. 145, 232.

Answer 1

Hint: We will find the HCF and LCM of the given numbers by using prime factorization method. We will first find the prime factors of the numbers and by grouping we will calculate the LCM and HCF.

Complete step by step solution:
We have been given numbers 145 and 232.
We have to find the LCM and HCF of given numbers.
We know that to find the LCM by prime factorization method first we need to write each number as the product of their prime factors. Then we will find the product with the highest power of all prime factors. The obtained product is the LCM of the numbers.
The prime factors of 145 are $145=5\times 29$
The prime factors of 232 are $232=2\times 2\times 2\times 29$
LCM of 145 and 232 will be
 $\begin{align}
  & \Rightarrow 2\times 2\times 2\times 5\times 29 \\
 & \Rightarrow 1160 \\
\end{align}$
Now, we know that HCF is the largest common factor of all given numbers.
Then we will get the HCF of 145 and 232 as
$\Rightarrow 29$
Hence we get the HCF and LCM of the given numbers as 29 and 1160 respectively.

Note:
Alternatively we can find the LCM by using the relation that the product of LCM and HCF is equal to the product of the given numbers. If we know the HCF of the given numbers then we can use the above formula.
Here in this question we get the HCF of 145 and 232 as 29. Then by using the relation we will get
$\text{LCM }\!\!\times\!\!\text{ HCF=product of two numbers}$
Substituting the values we will get
$\Rightarrow LCM\times 29=145\times 232$
Simplifying the above obtained equation we will get
$\begin{align}
  & \Rightarrow LCM\times 29=33,640 \\
 & \Rightarrow LCM=\dfrac{33640}{29} \\
 & \Rightarrow LCM=1160 \\
\end{align}$