Question

LCM of 30,45,12 By prime factorisation method

Answer 1

Answer:

180 is the right answer

Answer 2

Answer:

180

Step-by-step explanation:

question:

Find the LCM of 20 and 12 by prime factorization method.

Solution:

Step 1: To find LCM of 20 and 12, write each number as a product of prime factors.

30=3×2×5

12=2×2×3=2^2×3

45=3×3×5=3^2×5

Step 2: Multiply all the prime factors with the highest degree.

Here we have 3 with highest power 2 and other prime factors 2 and 5. Multiply all these to get LCM.

 Number of times each prime factor

   appears in the factorization of :

Prime  

Factor   Number  

30   Number  

12   Number  

45    L.C.M  

(max)  

2 1 2 0 2

3 1 1 2 2

5 1 0 1 1

LCM = 2^2 • 3^2 • 5

for knowledge :

The two principal methods which are used to find the LCM (Least Common Multiple) and the HCF (Highest Common Factor) of the numbers are the Prime Factorization Method and Division Method. Both the methods are explained here with many examples. We have provided the prime factors of the given numbers, such as 24, 12, 30, 100, etc. using these methods. Here, you will learn how to find the LCM and HCF of the numbers by both the approaches. Before that, let us discuss what is LCM and HCF in detail.

Least Common Multiple (LCM)

The least or smallest common multiple of any two or more given natural numbers are termed as LCM.

For example, LCM of 10, 15, and 20 is 60.

Highest Common Factor (HCF)

The largest or greatest factor common to any two or more given natural numbers is termed as HCF of given numbers. It is also known as GCD (Greatest Common Divisor).

For example, HCF of 4, 6 and 8 is 2.

How to Find LCM and HCF?

We can find HCF and LCM of given natural numbers by two methods i.e. by prime factorization method or division method. In the prime factorization method, given numbers are written as the product of prime factors. While in the division method, given numbers are divided by the least common factor and continue still remainder is zero.

Note: Prime numbers are numbers which have only two factors i.e. one and the number itself.

LCM by Prime Factorization Method

Here given natural numbers are written as the product of prime factors. The lowest common multiple will be the product of all prime factors with the highest degree (power).