Calculates the least common multiple of two or more numbers. natural numbers with our online math calculator, a tool that will allow you to know the smallest natural number that is a multiple of the numbers entered.
All you have to do is write the numbers separated by commas and click the Calculate button to obtain its least common multiple.
If you need it, we also have at your disposal a calculator of the greatest common divisor of two numbers.
How is the least common multiple calculated?
To know the least common multiple of two or more numbersit is necessary to perform the decomposition into prime factors of each one of them. That is to say, we are going to obtain the numbers (prime factors) that when multiplied together will give us as a result the starting number.
Once we have the decomposition of each number done, the least common multiple will be the result of multiplying the common and uncommon factors of numbers raised to the highest power.
That is, we have to:
- Take all prime factors that are not present in all numbers.
- Take the prime factor common to all the numbers and which has more power.
- Multiply all the numbers we have selected in the previous two steps.
In this example you can see how to calculate the least common multiple of 72 and 50 although as you can see for yourself, all these operations can be saved with our online m.c.m. calculator. Still, it is always good to know how to get the result we are looking for and where it comes from.
Least common multiple problems
As the theory is best understood with a practical example, we will calculating the least common multiple of numbers 72 and 50:
As we have said before, the first thing we have to do is to decompose each of the numbers into their prime factors. Therefore, we have to:
72 = 2 x 2 x 2 x 2 x 3 x 3 x 3 = 23 x 32
50 = 2 x 5 x 5 x 5 = 2 x 52
Now we look for non-common factors. In this case, we see that 32 and 52 meet this requirement, so we will write them down to multiply them later on.
To conclude, we look for common factors and we see that the 2 is present in both numbers but in the case of 72, we have it repeated 3 times so it is the one with the highest power.
Finally, we multiply all the prime factors that we have noted in the previous two steps and we have that the cfm of 72 and 50 is:
mcm (72.50) = 32 x 52 x 23 = 9 x 25 x 8 = 1800
This process can be applied in a similar way in the event that you need to calculate the least common multiple of 3 numbers4 numbers or whatever.
What is the least common multiple of 924 and 630?
Let's look at another exercise in which we are asked for calculate the least common multiple of the numbers 924 and 630. As they are quite large they cannot be solved mentally, so we will decompose each number into prime factors:
924 = 2 x 2 x 3 x 7 x 11
630 = 2 x 3 x 3 x 3 x 5 x 7
As uncommon factors we have 5, 7 and 11. Of the common factors we keep the ones that are raised to the maximum power, that is, 22 y 32.
Now we multiply them all together and the result will be the MCM:
22 x 32 x 5 x 7 x 11 = 13860
Least common multiple of fractions
In the case of fractions, the first thing we have to do is to search for the common denominator from their least common multiple.
Once you know which is the new denominator that will be present in all the fractions, tap replace the numerator of each fraction by its equivalent. To do this we divide the common denominator by the initial denominator.
With the result obtained we multiply by the initial numerator and obtain the new equivalent numerator of the fraction.
This must be repeated for all fractions involved in the addition or subtraction.
In the exercise that you have above these lines we see that the least common multiple of the fractions is 60. Therefore, when calculating the numerators we have that:
- First fraction: 60/4 = 15 → 15 x 2 = 30
- Second fraction: 60/3 = 20 → 20 x 6 = 120
- Third fraction: 60/5 = 12 → 12 x 3 = 36
And now we have it solved. As you have seen, it is essential to know cow to calculate the least common multiple for some operations with fractions.
Calculate the least common multiple in Excel
You can also use Excel as mcm calculator to get the least common multiple of the numbers you need.
To do this, open a new spreadsheet and in an empty cell type the following formula:
For example, if we want to calculate the least common multiple of 12 and 18we have to write the formula as follows:
And after pressing the enter key, it will appear that the MCM of these two numbers is 36.
How our MCM calculator works
Our least common multiple calculator works in a very simple way and will allow you to calculate the MCM of two numbers, three numbers, four numbers or any amount you want.
Just type each figure separated by a comma in the appropriate box and click the calculate button to get your MCM instantly.
Have you had any complication when calculating the least common multiple? Leave us a comment and we will try to help you as soon as possible.