Question

Find the LCM of
 $ 8{\text{ and 10}} $

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. Here, we will find factors directly since the given two numbers are very small.

Complete step-by-step answer:
In this prime factorization method, first we will find the factors of the given numbers by a division method where you have to start dividing the number with least prime numbers till the further division is not possible. Gradually try to divide the number first by $ 2 $ then $ 3,5,7,11 $ and so on...
By prime factorization-
 $ 8 = 2 \times 2 \times 2\;{\text{ }}....{\text{ (a)}} $
Similarly, prime factors for
 $ 10 = 2 \times 5\;{\text{ }}....{\text{ (b)}} $
Now, by observing the above two equations, we can see that factor $ 2 $ is common in both the equations. So, LCM is writing common factors and then the product of other factors.
$\Rightarrow$ LCM $ = 2 \times 2 \times 2 \times 5 $
$\Rightarrow$ LCM $ = 40 $

Note: Here, we have written prime factors directly since given numbers are very small but in case of large numbers use the division method or the prime factor tree method to get the prime numbers. Remember basic multiples of the numbers till twenty for an accurate and efficient solution. Common mistakes happen between the application of HCF and LCM concepts. Remember the basic difference between the HCF (Highest common factor) and LCM (Least common multiple) to solve these types of sums and apply accordingly. HCF is the greatest or the largest common factor between two or more given numbers whereas the LCM is the least or the smallest number with which the given numbers are exactly divisible.