Question

HCF and LCM of 6, 72 and 120 are
a) 120, 72
b) 6, 360
c) 72, 6
d) 3, 72

Answer 1

Hint: We have three numbers as 6, 72, and 120. We need to find the HCF and LCM of these numbers. So, by the prime factorization method, firstly find the factors of all the numbers. Then, find the common factors of all the numbers. That is the highest common factor (HCF) of all the numbers. Also, LCM is the product of higher power of the factors of the numbers. Now, multiply all the higher power of the factors of the numbers to get the LCM of 6, 72 and 120

Complete step-by-step solution:
We have the following numbers: 6, 72 and 120
Now, by prime factorization method, we get the prime factors of the numbers:
$\begin{align}
  & 6=2\times 3 \\
 & 72=2\times 2\times 2\times 3\times 3 \\
 & 120=2\times 2\times 2\times 3\times 5 \\
\end{align}$
So, we need to find the common factors of 6, 72 and 120
We get: $2\times 3=6$ as a common factor of 6, 72 and 120
Therefore, 6 is the HCF of 6, 72 and 120
Now, we need to find the LCM of 6, 72 and 120
Since the higher powers of all the factors of the numbers are: ${{2}^{3}},{{3}^{2}},{{5}^{1}}$
So, multiply all the higher powers of all the factors of the numbers, we get:
$\begin{align}
  & LCM={{2}^{3}}\times {{3}^{2}}\times {{5}^{1}} \\
 & =360
\end{align}$
Therefore, 360 is the LCM of 6, 72 and 120
Hence, option (b) is the correct answer.

Note: While finding the factors of the numbers, always be careful choosing a prime number as a factor. Because if we choose a composite number, which itself can be factorized further, it makes the solution lengthy. Therefore, always go with prime number, that’s what the prime factorization method means.