Question

Find the HCF and LCM of \[12,\,15,\,18,\,27\]?

Answer 1

Hint: Here the full forms of these abbreviated terms HCF and LCM are, Highest Common factor and Least Common Multiple, respectively. The HCF defines the greatest factor present in between the mentioned two or more numbers, whereas LCM defines the least number which is exactly divisible by two or more numbers.

Complete step-by-step solution:
H.C.F. of Two numbers = Product of Two numbers/L.C.M of two numbers
&
L.C.M of two numbers = Product of Two numbers/H.C.F. of Two numbers
But as per the question, we have to calculate HCF and LCM of 4 numbers so this formula cannot suffice, so we have to go either way.
Calculating HCF, we have to factorize following numbers, and we get:
\[
   \Rightarrow 12 = 2 \times \,2 \times 3 \\
   \Rightarrow 15 = \,3 \times 5 \\
   \Rightarrow 18 = \,2 \times 2 \times 3 \\
   \Rightarrow 27 = \,3 \times 3 \times 3 \]
HCF is the highest common factor, so looking at the common term here, that is 3, here as 3 can be seen as factors of all four numbers.
Therefore, HCF=3
Now, we will calculate LCM. When we factorize all the numbers together and we select the common factor which have most powers in factorisation, Hence we get LCM here it is equal to:
LCM=\[{2^2} \times {3^3} \times \,5 = 340\]

Note: There are two ways to solve such questions, that is the method of prime factorization and the method of division, the above question has been solved by using the method of prime factorization. HCF is also known as the greatest common factor and LCM is also called the Least Common Divisor.