Question 114689: How do you find the LCM of a number?Can you please give me a couple of examples to study also.THANKS
Answer by chitra(359)  (Show Source):
You can put this solution on YOUR website! Method 1
Simply list the multiples of each number (multiply by 2, 3, 4, etc.) then look for the smallest number that appears in each list.
Example: Find the least common multiple for 5, 6, and 15.
First we list the multiples of each number.
Multiples of 5 are 10, 15, 20, 25, 30, 35, 40,...
Multiples of 6 are 12, 18, 24, 30, 36, 42, 48,...
Multiples of 15 are 30, 45, 60, 75, 90,....
Now, when you look at the list of multiples, you can see that 30 is the smallest number that appears in each list.
Therefore, the least common multiple of 5, 6 and 15 is 30.
Find the least common multiple of 5, 6 and 15.
Factor into primes
Prime factorization of 5 is 5
Prime factorization of 6 is 2 x 3
Prime factorization of 15 is 3 x 5
Notice that the different primes are 2, 3 and 5.
Now, we do Step #1 - Count the number of times each prime number appears in each of the factorizations...
The count of primes in 5 is one 5
The count of primes in 6 is one 2 and one 3
The count of primes in 15 is one 3 and one 5
Step #2 - For each prime number, take the largest of these counts. So we have...
The largest count of 2s is one
The largest count of 3s is one
The largest count of 5s is one
Step #3 - Since we now know the count of each prime number, you simply - write down that prime number as many times as you counted for it in step 2.
Here they are...
2, 3, 5
Step #4 - The least common multiple is the product of all the prime numbers written down.
2 x 3 x 5 = 30
Therefore, the least common multiple of 5, 6 and 15 is 30.
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