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Procedure - Find the Least Common Multiple (LCM), Math, Class 9 | Extra Documents & Tests for Class 9 PDF Download

Procedure:

1. Prime factorisation method:

  • Factorise each number into its prime factors.
  • Count the number of times each prime factor appears in factorisation.
  • For each and every prime number take the highest power of prime factor.
  • The LCM of number is the multiple of factors having highest power.

ex.  Find the LCM of 16,20.

      16 = 2*2*2*2 = 2^4

      20 = 2*2*5  = 2²*5

LCM of 16 and 20 = 24 * 5 = 2*2*2*2*5= 80

2. Grid method:

  • Create a grid and write the numbers on top of grid separated by comma
    |  4, 6
    |
  • Divide the numbers with the smallest common prime factor.
    2 |  4, 6
    |  2, 3
  • Repeat the process until no more common factors exist.
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FAQs on Procedure - Find the Least Common Multiple (LCM), Math, Class 9 - Extra Documents & Tests for Class 9

1. What is the definition of the Least Common Multiple (LCM)?
Ans. The Least Common Multiple (LCM) is the smallest multiple that two or more numbers have in common. It is the lowest common multiple that can be divided evenly by all the given numbers.
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 either the prime factorization method or the method of listing multiples. In the prime factorization method, you express each number as a product of prime factors, and then write down the highest power of each prime factor that appears in any of the numbers. Multiply all these highest powers together to get the LCM. In the method of listing multiples, you list the multiples of each number until you find a common multiple.
3. Can you explain the prime factorization method in finding the LCM?
Ans. Sure! In the prime factorization method, you start by writing the given numbers as the product of their prime factors. Then, you write down the highest power of each prime factor that appears in any of the numbers. Finally, you multiply all these highest powers together to get the LCM. For example, let's find the LCM of 12 and 18. The prime factorization of 12 is 2^2 * 3^1, and the prime factorization of 18 is 2^1 * 3^2. The highest power of 2 is 2^2, and the highest power of 3 is 3^2. Therefore, the LCM of 12 and 18 is 2^2 * 3^2 = 36.
4. Is the LCM of two numbers always greater than or equal to the largest number?
Ans. Yes, the LCM of two numbers is always greater than or equal to the largest number. This is because the LCM is a multiple of both numbers, so it must be at least as large as the largest number. For example, if we find the LCM of 7 and 9, the LCM will be equal to or greater than 9.
5. Can the LCM of two numbers be smaller than both numbers?
Ans. No, the LCM of two numbers cannot be smaller than both numbers. The LCM is always a multiple of both numbers, so it must be at least as large as the larger number. If the LCM were smaller than both numbers, it wouldn't be a common multiple.
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