Question

Find the LCM of the given numbers by prime factorisation method: 24, 28, 196.

Answer 1

Hint: Here, we have to use the concept of the factorization and LCM (Lowest common multiple). Factorization is the process in which a number is written in the forms of its factors which on multiplication give the original number. After the factorization we will take each factor and its maximum occurrence to find the LCM. So by using the concept of factorization we will be able to find out the LCM of the given numbers.

Complete step-by-step answer:
Firstly we have to find out the factors of the given numbers i.e. 24, 28, 196.
Factors are the smallest numbers with which the given number is divisible and their multiplication will give the original number.
So, factors of the number 24 are \[2 \times 2 \times 2 \times 3\].
Similarly we will find the factors of the other two numbers i.e. 28 and 196.
Factors of the number 28 are\[2 \times 2 \times 7\].
Factors of the number 196 are\[2 \times 2 \times 7 \times 7\] .
Now, to find out the LCM of the numbers we will take each factor with their maximum number of occurrences in a number. For example, factor 2 occurs three times maximum, number 3 which occurs one time maximum and number 7 occurs two times maximum.
Therefore, LCM of the numbers 24, 28, 196 is \[2 \times 2 \times 2 \times 3 \times 7 \times 7 = 1176\].
So, the LCM of the given numbers i.e. 24, 28, 196 is 1176.

Note: LCM (Least Common Multiple) of the given numbers is the smallest number which is the multiple of the given numbers. HCF (Highest common factor) of the given numbers is the highest factor which is common in the given numbers. HCF (Highest common factor) is also known as the Greatest common factor. HCF of the numbers is generally less than or equal to the LCM of the number. Product of the LCM and the HCF of some numbers is equal to the product of the original numbers.