Question

Consider the numbers 18 and 27.
Factors of \[18 = 2 \times 3 \times 3\]
Factors of \[27 = 3 \times 3 \times 3\]
LCM of \[18, 27 = 3 \times 3 \times 3 \times 2 = 54\]
HCF of \[18, 27 = 3 \times 3 = 9\]
\[LCM \times HCF = 54 \times 9 = 486 \]
Product of 18 and 27 = 486.
What do you notice?

Answer 1

Hint: Given are the two different numbers. Also there mentioned the factors. After that they found the LCM and HCF of the numbers. The product of the LCM and HCF is equal to the product of two numbers so given.

Complete step by step solution:
Given the question is totally solved and we have to conclude the result. So we will check the given data step by step.
Very first there are the two numbers given and their factors are also given. But the factors are the product of prime numbers only.
Then LCM and HCF of the numbers are found using the prime factors method.
Then we can observe from the given last few data steps that “ product of two numbers is equal to the product of their HCF and LCM itself”.

Note: Note that HCF and LCM are the terms related to factors of a number. Highest common factor and lowest common multiple. But only difference is HCF is the product of common factors only whereas LCM is the product of common and uncommon factors also. In the question above the conclusion is very clear because it is given in the last two lines separately.