what is LCM ? tell meine example of LCM to understand
Answers
Answer.
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Step-by-step explanation:
Basically, the common multiple is a number which is a multiple of two or more numbers. L.C.M is used to determine the least common factor or multiple of any two or more given integers. For example, L.C.M of 16 and 20 will be 2 x 2 x 2 x 2 x 5 = 80, where 80 is the smallest common multiple for numbers 16 and 20.
Answer:
Least Common Multiple(LCM) is a method to find the smallest common multiple between any two or more numbers. Basically, the common multiple is a number which is a multiple of two or more numbers. L.C.M is used to determine the least common factor or multiple of any two or more given integers. For example, L.C.M of 16 and 20 will be 2 x 2 x 2 x 2 x 5 = 80, where 80 is the smallest common multiple for numbers 16 and 20. Now, if we consider the multiples of 16 (16,32,48,64,80,..) and 20 (20,40,60,80,..) we can see that the first common multiple for both the numbers is 80. This proves the method of LCM as correct.
Example with explanation:
As we have already discussed, the least common multiple is the smallest common multiple for any two or more given numbers.
A multiple of a number we get, when we multiply a number with another number. Like 4 is a multiple of 2, as we multiply 2 with 2, we get 4. Similarly, in the case of maths table, you can see the multiples of a number when we multiply them from 1,2,3,4,5,6 and so on but not with zero. Now, if we have to find the common multiple of two or more numbers, then we have to write all the multiples for the given numbers. Say for example, if there are two numbers 4 and 6, then how to find the common multiple between them?
Let us write multiples of 4 and 6 first,
4 : 4,8,12,16,20,24,28,…..
6: 6,12,18,24,30,36,42…..
From the above two expressions you can see, 4 and 6 have common multiples as 12 and 24. They may have more common multiple if we go beyond. Now, the smallest or least common multiple for 4 and 6 you can see here is 12. Therefore, 12 is the L.C.M of 4 and 6.
Now, let us take an example of 3 numbers.
Example: Find the L.C.M 4,6 and 12.
Solution: First write the common multiples of all the three numbers.
Common Multiples of 4 : 4,8,12,16,20,24,28,…..
Common Multiples of 6: 6,12,18,24,30,36,42…..
Common Multiples of 12: 12,24,36,48,60,72,….
From the above-given multiples of 4, 6 and 12, you can see, 12 is the smallest common multiple.
Therefore, L.C.M. of 4, 6 and 12 is 12.
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