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.

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

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.

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.

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.

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.

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).

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,

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 5x2= 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.

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

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= 3x5

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

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.

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.

2x7= 14

So the HCF of 42 and 70 is 14.