Lowest common multiple (LCM) and Highest Common Factor (HCF) are

the most used methods of Mathematics and also the most important as they are

used in finding the solution of many other question’s solution. With these

shortcut methods, you can easily solve LCM and HCF of

two or more numbers in your mind in seconds.

the most used methods of Mathematics and also the most important as they are

used in finding the solution of many other question’s solution. With these

shortcut methods, you can easily solve LCM and HCF of

two or more numbers in your mind in seconds.

So here are the shortcut methods or formulas of finding the LCM and HCF

of numbers

of numbers

When you practice this method, you can easily solve this type of questions in your mind. The below give method can easily be used to

solve LCM of numbers in seconds without the use of paper work.

solve LCM of numbers in seconds without the use of paper work.

Here is an example.

Suppose you are given a question:

Find the LCM of 12, 18?

Now here is the shortcut formula for solution of LCM of two

numbers or more numbers given above.

numbers or more numbers given above.

Step 1:

pick the highest of the given numbers of whom we

have to find the LCM.

pick the highest of the given numbers of whom we

have to find the LCM.

In the above example question, pick 18 as it is highest

among 12 and 18.

among 12 and 18.

Step 2: check it whether it can be divided by other number(s).

if you can divide it, then it means your answer is that highest number. But if

you cannot divide it by other number(s), then follow the step 3 given below.

if you can divide it, then it means your answer is that highest number. But if

you cannot divide it by other number(s), then follow the step 3 given below.

In the above example, check 18 whether it can be divided by 12

or not. Since 18 cannot be divided by 12, so move on to step 3.

or not. Since 18 cannot be divided by 12, so move on to step 3.

Step 3: multiply the highest number to 2,3,4,… and so on

till you find that number which can also be divided by the other number(s).

till you find that number which can also be divided by the other number(s).

In the above problem, multiply 18 to 2 in your mind, it is

equal to 36. Now check it whether it can be divided by 12. Since 36 can be

divided by 12,

equal to 36. Now check it whether it can be divided by 12. Since 36 can be

divided by 12,

so 36 is the LCM of 12,18.

Now let us take another example.

Find the LCM of 2, 3, 5?

Shortcut formula: pick 5 since it is highest number among

the three. Now check it whether it can be divided by 2 and 3. 5 cannot be

divided by 2 and 3. Now think of 5×2= 10 (since you know the table of 5). Check

whether it can be divided by 2 and 3. It again cannot be divided. Now think of

15 then 20 then 25 then 30. Now 30 is that number which can be divided by 2 and

3.

the three. Now check it whether it can be divided by 2 and 3. 5 cannot be

divided by 2 and 3. Now think of 5×2= 10 (since you know the table of 5). Check

whether it can be divided by 2 and 3. It again cannot be divided. Now think of

15 then 20 then 25 then 30. Now 30 is that number which can be divided by 2 and

3.

So the LCM of 2, 3, 5 is 30.

When you practice this method, you can easily solve LCM of

numbers in seconds in your mind.

numbers in seconds in your mind.

Here is an alternate basic method.

Find all the factors of numbers. Now multiply

the prime factors but the common prime factors should be multiplied

the prime factors but the common prime factors should be multiplied

For example

Find LCM of 12, 15?

The prime factors of 12 are 2, 2 and 3 because 12= 2x2x3

The prime factors of 15 are 3 and 5 because 15= 3×5

Now multiply each prime factor but the common prime factors

should be multiplied once i.e. since 3

is common prime factor among the factors given above, so we will multiply 3

only once. So the LCM of 12 and 15 is 2x2x3x5= 60

should be multiplied once i.e. since 3

is common prime factor among the factors given above, so we will multiply 3

only once. So the LCM of 12 and 15 is 2x2x3x5= 60

Shortcut method of finding HCF (Highest common factor)

To find the HCF of numbers, first prime factors of given

numbers. Now multiply all the common prime factors.

numbers. Now multiply all the common prime factors.

Let us take an example.

Find the HCF of 42, 70?

Solution: list the prime factors of both numbers.

42= 2x3x7

70= 2x5x7

Now find the common prime factor. The common prime factors

are 2 and 7. So multiply 2 and 7.

are 2 and 7. So multiply 2 and 7.

2×7= 14

So the HCF of 42 and 70 is 14.

This article is originally published by AnilJi.in.