Least Common Multiple


 
 
Concept Explanation
 

Least Common Multiple

Least Common Multiple:

What are the common multiples of 4 and 6 ? They are 12, 24, 36,..... . Which is the lowest of these? It is 12. We say that lowest common multiple of 4 and 6 is 12. It is the smallest number that both the numbers are factors of this number.

The lowest Common Multiple (LCM) of two or more given numbers is the lowest ( or smallest or least ) of their common  multiples.

Example:   Find the LCM of 12 and 18.

Solution    We know that common multiples of 12 and 18 are 36, 72, 108 etc.

The lowest of these is 36. Let us see another method to find LCM of two numbers.

 The prime factorisations of 12 and 18 are:

  12=2times 2times 3;;;18=2times 3times 3

In these prime factorisations, the maximum numbe of times the prime factor 2 occurs is two; this happens for 12. Similarly, the maximum number of times the factor 3 occurs is two; this happen for 18. The LCM of the two numbers is the product of the prime factors counted the maximum number of times they occur in any of the numbers. Thus, in this case LCM = 2times 2times 3times 3=36.

 

Sample Questions
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Question : 1

Micheal and Martin collect hockey cards. Micheal has 45 cards in his collection and Martin has 30 cards in his collection. If the cards in collection of both boys come in packages of the same number of cards, then how many cards of each of them can be packed of equal numbers ?

Right Option : A
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Question : 2

A prime number has two factros 1 and the number itself. Which one of the following is correct about the prime factors of greatest number of two digit?

Right Option : C
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Question : 3

Given below is the procedure to find the L.C.M by prime factorisation method.

  • A: Select the greatest power of every prime factor.
  • B: Express each number as a product  of prime factors .
  • C: The product of these prime factors with their greatest power is the L.C.M of the given numbers.

Reat the steps by step procedure and arrange the correct order of steps by choosing the correct option.

Right Option : C
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