Question

What is the difference between LCM and HCF of $20\;{\text{30}}\;{\text{40?}}$

Answer 1

Hint:To solve this problem, first we will find the prime factors of all the three given numbers. Then will observe the resultant factors and note down the common factors from all the three numbers and accordingly find the LCM and HCF. Here, we will find factors by prime factorization method.

Complete step by step answer:
First find the prime factorization – first of all we will find the factors of the given numbers by factorization method where you have to start dividing the number with least prime numbers until further division is not possible. Progressively try to divide numbers first by $2$ then $3,5,7,11$ and so on...
Take all the three given terms –
$20 = 2 \times 2 \times 5 \\
\Rightarrow 30 = 2 \times 3 \times 5 \\
\Rightarrow 40 = 2 \times 2 \times 2 \times 5 \\ $
Now, the LCM (Least common multiple) in the above three equations are given by the common factor along with other factors.
Therefore, LCM$ = 2 \times 2 \times 2 \times 3 \times 5$
Simplify the above expression -
LCM$ = 120$
Similarly, the HCF (Highest common factor) in the above three equations is $ = 2 \times 5 = 10$.

Therefore, the required answer - LCM and HCF of $20,30$ and $40$ are $120$ and $10$.

Note: Know the difference between the HCF and LCM properly and apply accordingly. HCF is defined as the greatest or the largest common factor between two or more given numbers whereas the LCM is defined as the least or the smallest number with which the given numbers are exactly divisible. Remember the concept of division and the multiples of the numbers at least till twenty. Factorization can also be done by using the division method or the factor tree method.