The Least Common Multiple

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined...4 years ago. Least Common Multiple Of 12 And 15. To get LCM you want to multiply 12 and 15 until you get a common number. The answer would be 60. Lowest Common Multiple is the lowest product of numbers that are common between two or more numbers.The least common multiple (LCM) of a group of numbers is the smallest number that is a multiple of all the numbers. Write out the first several multiples of the first number. A multiple is a product of any number and an integer.[1] X Research source In other words, they are the numbers you would...Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.This video lesson addresses the least common multiple, or LCM. The LMC of two numbers is the smallest value divisible by both the numbers Then, pick the least of all multiples that are they have in common. For example, find the LCM (least common multiple) of 12 & 16.

What is the LCM (Lowest Common Multiple) of 12 and 15?

The least common multiple of two numbers is 84, and one of the numbers is 5 less than the other number. Find lowest common Multiple of given Number = Multiply of these number / GCD of the numberLowest Common Divisor (LCM) for example 4,5,6,7.This is the case with common multiple and least common multiple (LCM). A common multiple is a multiple that two or more numbers have in common. You can probably guess what a least common multiple is! To get more information about these terms, check out this tutorial!The fastest way to find the least common multiple (and also the least common denominator) is usually to start naming the multiples of the largest number. For each multiple, check to see if the other numbers can also go evenly into that multiple.The Least Common Multiple (LCM) of the numbers 6, 4 is 12.

4 Ways to Find the Least Common Multiple of Two Numbers - wikiHow

The least common multiple is sometimes referred to as the lowest common multiple and abbreviated as (LCM). For instance, the LCM of 2, 3, and 7 is 42 because 42 is a multiple of 2, 3 How to Find the Least Common Multiples? The LCM of two or more numbers can be found by various methods.Least Common Multiple (LCM) Find the LCM by listing the multiples of each number and find the smallest one that is common. Example: What is the least common multiple (lcm) of 15, 6, and 10?The least common multiple of two integers a and b is the smallest positive integer that is divisible by both a and b. By "least," we For this explanation, we will refer to the least common multiple of a and b as LCM(a, b), but the notation "LCM" is not something you need to know for GMAT questions.The Least Common Multiple (L.C.M.) of two numbers is the lowest number that can be divided both. It can be used to find the lowest common denominator when adding or subtracting fractions. Don't let the "least" in the name fool you - the LCM is no smaller than the largest of the numbers.This is the LCM. Example 3. Find the lowest common multiple of 6 and 9. List the multiples of 8 and stop when you find a multiple of both 5 and 6.

The smallest positive number that is a multiple of two or extra numbers.

Let's start with an Example ... 

Least Common Multiple of 3 and 5:

List the Multiples of every quantity,

The multiples of 3 are 3, 6, 9, 12, 15, 18, ... and so onThe multiples of Five are 5, 10, 15, 20, 25, ... and many others

Find the first Common (similar) worth:

The Least Common Multiple of 3 and 5 is 15

(15 is a multiple of each 3 and 5, and is the smallest quantity like that.)

So ... what is a "Multiple" ?

We get a multiple of a host after we multiply it through every other number. Such as multiplying via 1, 2, 3, 4, 5, and so on, however not 0. Just like the multiplication desk.

Here are some examples:

The multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,... The multiples of 5 are: 5,10,15,20,25,30,35,40,45,50,...

What is a (*6*) ?

Say we've indexed the first few multiples of 4 and 5: the common multiples are those which are found in both lists:

The multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,... The multiples of 5 are: 5,10,15,20,25,30,35,40,45,50,...

Notice that 20 and 40 seem in both lists? So, the common multiples of 4 and 5 are: 20, 40, (and 60, 80, etc ..., too)

What is the "Least Common Multiple" ?

It is simply the smallest of the common multiples.

In our previous instance, the smallest of the common multiples is 20 ...

... so the Least Common Multiple of 4 and 5 is 20.

Finding the Least Common Multiple

List the multiples of the numbers until we get our first match.

Example: Find the least common multiple of 4 and 10:

The multiples of 4 are: 4, 8, 12, 16, 20, ...and the multiples of 10 are: 10, 20, ...

Aha! there is a match at 20. It looks like this:

So the least common multiple of 4 and 10 is 20

Example: Find the least common multiple of 6 and 15:

The multiples of 6 are: 6, 12, 18, 24, 30, ...and the multiples of 15 are: 15, 30, ...

There is a fit at 30

So the least common multiple of 6 and 15 is 30

More than 2 Numbers

We can also in finding the least common multiple of three (or more) numbers.

Example: Find the least common multiple of 4, 6, and 8

Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, ...Multiples of 6 are: 6, 12, 18, 24, 30, 36, ...Multiples of 8 are: 8, 16, 24, 32, 40, ....

So 24 is the least common multiple (I can't discover a smaller one!)

Hint: We could have smaller lists for the larger numbers.

Least Common Multiple Tool

There is another means: the Least Common Multiple Tool does it automatically. (Yes, we waited till the finish to tell you!)

 

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