Least Common Multiple
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:
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 = .
In which of the following Prime Factorisation is not completed ? | |||
| Right Option : D | |||
| View Explanation | |||
L.M.C. of 12, 24 and 36 is _______________ | |||
| Right Option : C | |||
| View Explanation | |||
Four bells ring at intervals of 6, 7, 8 and 9 seconds respectively. All the bells ring together after ________________ seconds. | |||
| Right Option : A | |||
| View Explanation | |||
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