What is LCM

It is simply the smallest of the common multiples.

For Example, what is LCM of 3 and 5?

The multiples of 3 are 3, 6, 9, 12, 15, 18, ...

The multiples of 5 are 5, 10, 15, 20, 25, ...

Find the first Common (same) value which is 15

So the Least Common Multiple of 3 and 5 is 15

LCM stands for the least common multiple or the lowest common multiple in math. The least common multiple of two or more numbers is the smallest number among all common multiples of the given numbers. Let's look at an example for a better understanding: let's look at 2 numbers: 3 and 7. Each has their own set of multiples:

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27,...

Multiples of 7: 7, 14, 21, 28, 35, 42,...

By looking at their multiples, we can notice that the first common multiple for 3 and 7 is 21. This is the least common multiple for 3 and 7. This is called the Listing Method which basically means listing a few multiples of each number until the lowest common multiple (LCM) is found. This method is used generally for low numbers where the LCM can be found only after a few listed multiples.

Another method available for finding LCM is by Prime Factorization Method, which is the most popular method as it is applicable for any number, low or high. The steps to be followed to use this method are the following:

• Step 1: Find the prime factors of the given numbers by repeated division method.
• Step 2: Write the numbers in their exponent form. Find the product of only those prime factors that have the highest power.
• Step 3: The product of these factors with the highest powers is the LCM of the given numbers.

In order to understand better this method, let's look at an example:

Example: Find the least common multiple (LCM) of 50 and 120 using prime factorization.

Solution: Let us find the LCM of 50 and 120 using the prime factorization method.

• Step 1: The prime factorization of 50 and 120 are: 50 = 2 × 5 × 5 and 120 = 2 × 2 × 2 × 3 × 5
• Step 2: If we write these prime factors in their exponent form it will be expressed as 50 = 2¹ × 5 ²  and

120 = 2³ × 3 × 5

• Step 3: Now, we will find the product of only those factors that have the highest powers among these. This will be: 2³ × 3¹ × 5² = 8 × 3 × 25 = 600

Therefore, LCM of 50 and 120 is = 600.

Lowest Common Multiple! An LCM between two numbers is the smallest number that is a multiple of both. For example, between 6 and 7, the LCM would be 42, as this is the smallest number that is a multiple of both!

LCM stands for lowest common multiple. LCM is a number which can be divisible by a set of numbers. For example, 12 is the LCM of 1, 2, 3, 4, 6 and 12. This means 12 can be divided exactly by 1, 2, 3, 4, 6, and 12 itself.

LCM stands for Lowest Common Multiple. This consists of finding a common number multiplied a certain times for two numbers.

LCM is the lowest common multiple of two or more numbers. You find it by going through the multiplication table (times table) of each number. The first number that appears on the times table of each number is the LCM.

For example, the LCM of 6 and 8 is 24

Here is how I worked it out

6 x 1 = 6

6x 2 = 12

6x 3 = 18

6 x 4 = 24

6 x 5 = 30

8 x 1 = 8

8 x 2 = 16

8 x 3 = 24

Hi Iftikhar,

Lcm is the abbreviation of Least common multiple. It's the smallest multiple that two or more numbers have in common.

Example:

LCM of 3 and 12 is 12.

because the multiples of 3 are:

3, 6, 9, 12, 15, 18, 21, 24, ..

and multiples of 12 are:

12, 24, 36, ....

Therefore the least common multiple (LCM) of 3 and 12 is 12.

LCM stands for Lowest Common Multiple.

This is the lowest multiple that 2 integers share.

For example, the lowest common multiple of 2 and 3 is 6.

Lowest Common Multiple

Given some numbers, could be 2 or more, we need to find the smallest number that is a multiple of all the numbers in your list.

For example -

1) 10 and 15

The lowest common multiple is 30 since, 30 is a multiple of both 10 (i.e. 10 x 3 = 30) and 15 (i.e. 15 x 2 = 30).

2) 6, 8 and 14

The lowest common multiple is 168 since, 168 is a multiple of both 10 (i.e. 6 x 28 = 168), 15 (i.e. 8 x 21 = 168) and 14 (i.e. 14 x 12 = 168).

There is three popular ways of finding this number:

1) Exhaustive method. Make a list of all the multiples of all numbers and find the first common multiple.

2) Finding the prime factors of the all numbers and with that you can find your answer. (You need a whole lesson to understand this)

3) Venn diagram method. (You need a whole lesson to understand this)

LCM stands for Lowest Common Multiple.

To explain the words:

Lowest => Smallest

Common => To have something in 'common', the Multiple (see next) will apply to both or all of the numbers in question. The number we are trying to find will be in the times-tables of the numbers we are given.

Multiple => think 'multiplication', so the multiple will normally be a large number, greater than or equal to one of the numbers in question.

In the 2 examples below we will look at finding the LCM using lists of times-tables.

For more comples numbers, or trying to find the LCM of more than 2 numbers, finding the prime factors (a recap on prime factors would be ideal before using this method) would be more efficient.

Example 1:

Find the LCM of 4 and 12.

We want to find the smalllest number in the times-tables of 4 and 12.

There are several methods to find the LCM. If the numbers are small (1 or 2 digits), one option is to write out the times-tables of 4 and 12 and see which one is the first in both numbers:

4 times-tables: 4, 8, 12, 16, 20, . . .

12 times-tables: 12, 24, 36, 48, . . . .

Looking at the list of numbers, the first number in both times-tables is 12: 3x4 = 12 and 1x12 = 12.

So the LCM of 4 and 12 is 12.

Example 2:

Find the LCM of 6 and 8:

** A common misconception may be to multiply the given numbers together. While this would give a multiple, and would sometimes be the lowest (such as with numbers 3 and 4, with an LCM of 12), this is not true for most cases, as we will see here.

6 times-tables: 6, 12, 18, 24, 30, 36, . . .

8 times-tables: 8, 16, 24, 32, 40, . . .

From the lists above, we can see that the lowest (smallest) number (multiple) in both lists (therefore in 'common') is 24.

So the LCM of 6 and 8 is 24.

(Note that by multiplying the given numbers, 6 x 8, we get 48, which is NOT the LCM).

For future lessons and more complex examples we would recap prime numbers and then look at finding the LCM using 'prime factor trees'.

Lcm is least common multiple which means it's the smallest multiple what two or more numbers have in common for eg .. take 2 numbers , number 2 and 3 . Multiple of 2 are 2,4,6,8 and so on and multiple of 3 are 3,6,9 and so on now the common and smallest number is 6 . So 6 is the lcm

Lowest common multiple, numbers are shared between 2 or more numbers eg. the lowest common multiple of 2 and 4 is 4

LCM stands for lowest common multiple. This is the lowest number that can be divided into two or more different numbers equally. For example, the lowest common multiple of 12 and 15 is 3 because it is the smallest number that can be divided into 12 and 15 equally with nothing left over.

LCM stands for Least Common Multiple. The lowest common multiple numbers from 2 or more numbers. For example, LCM of 4 and 5 is

The multiples of 4 are 4, 8, 12, 16, 20, 24 ....

The multiples of 5 are 5, 10, 15, 20, 25....

here in both cases, the common number is 20. So. The LCM of 4 and 5 is 20, which is the least common in both 4 and 5.

Least/Lowest Common Multiple. The smallest positive integer that is divisible by both A and B. For example - if it was for 4 and 6, the LCM would be 2.