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Theory - Find the Least Common Multiple (LCM), Math, Class 9 PDF Download

Objective:

Find the Least Common Multiple (LCM).

Theory:

Definition of LCM:The least common multiple(LCM) of two integers is the smallest positive integer that is divisible by both the integers.

There are two main methods to find the lcm

    1. Prime factorisation method

    2. Grid method

Prime factorisation method: The prime factors of a positive integer are the prime numbers that divide that integer exactly. The prime factorization can be written in way as the order of factors does not matter.

ex. prime factors of 48 = 2*2*2*2*3

Grid method:  The grid method of LCM is an easy approach to find the LCM, i.e. We find the LCM of numbers using grid.

ex.        2 |  4, 6

             2 |  2, 3

             3 |  1, 3

                |  1, 1

LCM of 4 and 6 is 2*2*3=12

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FAQs on Theory - Find the Least Common Multiple (LCM), Math, Class 9

1. What is the definition of the Least Common Multiple (LCM)?
Ans. The Least Common Multiple (LCM) is the smallest positive multiple that two or more numbers have in common. In other words, it is the smallest number that is divisible by each of the given numbers without leaving a remainder.
2. How do you find the LCM of two or more numbers?
Ans. To find the LCM of two or more numbers, you can use the prime factorization method. Firstly, express each number as a product of its prime factors. Then, take the highest power of each prime factor that appears in any of the numbers and multiply them together. The result will be the LCM.
3. Is the LCM of two numbers always greater than or equal to the numbers themselves?
Ans. Yes, the LCM of two numbers is always greater than or equal to the numbers themselves. This is because the LCM is a multiple of both numbers, and any multiple of a number is always greater than or equal to the number itself.
4. Can the LCM of two numbers be smaller than their greatest common divisor (GCD)?
Ans. No, the LCM of two numbers cannot be smaller than their greatest common divisor (GCD). In fact, the LCM is always equal to the product of the two numbers divided by their GCD. Therefore, the LCM is always greater than or equal to the GCD of the two numbers.
5. How does finding the LCM help in solving problems involving fractions?
Ans. Finding the LCM is crucial in solving problems involving fractions because it allows us to find a common denominator. By finding the LCM of the denominators of different fractions, we can convert them into fractions with the same denominator. This makes it easier to perform operations such as addition, subtraction, multiplication, and division with fractions.
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