Question

Find the L.C.M of the given numbers by prime factorization method: 36, 40, 126

Answer 1

Hint:
Here, we have to use the concept of factorization and LCM (Lowes common multiple). Factorization is the process in which a number is written in the form of its small factors which on multiplication give the original number. After factoring the given numbers we will take each factor and its maximum occurrence to find the LCM.

Complete Step by step Solution:
Firstly we have to find out the factors of the given numbers i.e. 36, 40, 126.
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 36 are \[2 \times 2 \times 3 \times 3\]
Similarly, we will find the LCM of the other number i.e. 40.
Factors of the number 40 are \[2 \times 2 \times 2 \times 5\]
Similarly, we will find the LCM of the other number i.e. 126.
Factors of the number 126 are \[2 \times 3 \times 3 \times 7\]
Now, to find out the LCM of the numbers we will take each factor with their maximum number of occurrences in a number i.e. factor 2 which occurs three times, number 3 which occurs two times maximum, number 5 which occurs one-time, and number 7 which occurs one-time only.
Therefore, LCM of the numbers 36, 40 and 126 is \[2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 7 = 2520\]

So, the LCM of the given numbers i.e. 36, 40 and 126 is 2520.

Note:
Here we should note that LCM (Least Common Multiple) of the given numbers is the smallest number which is the multiple of the given numbers. LCM is also commonly known as Least Common Divisor. 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.
The product of the LCM and the HCF of some numbers are equal to the product of the original numbers.