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# Least Common Multiple...?

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The next type of word problem we will consider in this video lesson is the one involving the least common multiple , the smallest multiple shared between two numbers. For example, 20 is the least common multiple between 4 and If we list the multiples for each number, we would find that the first number they have in common is The list of multiples for the number 4 is 4, 8, 12, 16, 20, 24, etc.

The list of multiples for the number 10 is 10, 20, 30, etc. A typical word problem that you might encounter that involves the least common multiple may sound like this one:. What is the least number of candies that both can split between the same number of people?

In this word problem, the least number of candies equals the number of people to be shared with, and also equals the least common multiple. So, we can find our answer by listing our multiples and then finding the first number that they have in common. Mike can split his candies between first 6 people, then 12 people, then 18, 24, 30, and so on.

Jenny can share her candies with 15 people at first, then 30, then 45, and so on. What is the first number they have in common? So, 30 is our answer. To unlock this lesson you must be a Study. Did you know… We have over college courses that prepare you to earn credit by exam that is accepted by over 1, colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

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Year Expiration Year is required. This process will explain how to find the least common multiple lcm for a given set of numbers. The multiples of 12 are 12x1, 12x2, 12x3, 12x4, 12x5, 12x6, 12x8, 12x9 and 12x The multiples of 15 are 15, 30, 45, 60, 75, 90,,,, Examine the list and find the common multiples from 12 and You can see 60 and show up in both lists. So which is the least of the common multiples?

Finding LCM for a set of numbers by the above method is bit cumbersome to do every time.

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For example 6 is the smallest multiple of both 2 and 3. Therefore, LCM of 2 and 3 is 6. Let’s try to find least common multiple of 3 and 4. Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, As we can see 12 and 24 both are the multiples of 3 and 4 but 12 is the smallest common multiple.

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The common multiples of 3 and 4 are 0, 12, 24, . The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both. Homework Help | Pre-Algebra | Factoring.