What is least common multiple?
Least common multiple is the smallest number which is a multiple of the given numbers.
Let us list out the positive integers which are the common multiples of 2 and 3.
6, 12, 18, 24, ............
In the above list, 6 is the first positive integer which is being a common multiple of 2 and 3.
Is there any positive integer less than 6 which is a common multiple of 2 and 3.
The answer is NO.
6 is the smallest positive integer which is a common multiple of 2 and 3.
Therefore, 6 is the least common multiple of 2 and 3.
The process of finding the least common multiple of prime numbers is pretty easy. We have to multiply the given prime numbers and the product is the least common multiple.
In each case, find the least common multiple of the given numbers.
Example 1 :
3 and 5
Solution :
The numbers 3 and 5 are prime numbers.
Therefore, the least common multiple of 3 and 5 is
= 3 x 5
= 15
Example 2 :
5 and 7
Solution :
The numbers 5 and 7 are prime numbers.
Therefore, the least common multiple of 5 and 7 is
= 5 x 7
= 35
Example 3 :
11 and 13
Solution :
The numbers 11 and 13 are prime numbers.
Therefore, the least common multiple of 11 and 13 is
= 11 x 13
= 143
Example 4 :
17 and 19
Solution :
The numbers 17 and 19 are prime numbers.
Therefore, the least common multiple of 17 and 19 is
= 17 x 19
= 323
Example 5 :
23 and 29
Solution :
The numbers 23 and 29 are prime numbers.
Therefore, the least common multiple of 23 and 29 is
= 23 x 29
= 667
Example 6 :
2, 3 and 5
Solution :
The numbers 2, 3 and 5 are prime numbers.
Therefore, the least common multiple of 2, 3 and 5 is
= 2 x 3 x 5
= 30
Example 7 :
5, 7, 11 and 13
Solution :
The numbers 5, 7, 11 and 13 are prime numbers.
Therefore, the least common multiple of 5, 7, 11 and 13 is
= 5 x 7 x 11 x 13
= 5005
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