How to find Least Common Multiple (LCM) of numbers

 How to find Least Common Multiple (LCM) of Numbers

METHOD 1:

STEP 1: Write multiples of given numbers.

STEP 2: List common multiples

STEP 3: The smallest common multiple is the LEAST COMMON MULTIPLE or LCM of given numbers.

Click here to see the solved example of this method.

METHOD 2:

Let us understand this method by an example.

EXAMPLE: Find Least Common Multiple (LCM) of 16 and 32.

SOLUTION:

STEP 1: Find a number which divides both 16 and 32, leaving no remainder.

It is recommended to start from 2, 3, 4….. one-by-one and check which divides all given numbers, leaving no remainder.

Now, 2 divides both 16 and 32, leaving no remainder.

16 ÷ 2 = 8

32 ÷ 2 = 16

STEP 2: Make table like this

STEP 3: Now again, as did in STEP 1, find a number that divides both 8 and 16, leaving no remainder  

Again, 2 divides both 8
and 16.

8 ÷ 2 = 4

16 ÷ 2 = 8

STEP 4: Extend the table like this:

STEP 5: Proceed in the
same way until you get all 1 in the right column. 

(Observe that in second last step when we have 1 and 2, drop down 1 as it is. Find a number that divides 2, leaving no remainder.

STEP 6: Multiply all
the numbers in the left column.

2×2×2×2×2= 32

Hence, LCM of 16 and 32
is 32.

FACT 1:

If one number is a multiple of other number, then the bigger number is their Least Common Multiple (LCM).

In the above solved example, we see 32 is Least Common Multiple (LCM) of 16 and 32 because 32 is a multiple of 16. 

FACT 2:

If the given numbers are different/distinct PRIME NUMBERS, then their product is their Least Common Multiple (LCM).

EXAMPLE: Find Least Common Multiple (LCM) of 7 and 13.

SOLUTION:

7 and 13 are distinct prime numbers

7 × 13 = 91

So, Least Common multiple (LCM) of 7 and 13 is 91.

FACT 3:

If of the two given numbers, one is a prime number and the other is neither prime number nor other number’s multiple, then their product is their Least Common Multiple (LCM).

EXAMPLE: Find Least Common Multiple (LCM) of 3 and 10.

SOLUTION:

Now

i) 3 is a prime number.

ii) 10 is not a prime number and 10 is not a multiple of 3  

So, Least Common Multiple (LCM) of 3 and 10 is 3 × 10 = 30.

FACT 4:

If the two given numbers are CONSECUTIVE, then their product is their Least Common Multiple (LCM).

The numbers are Consecutive if they follow each other in order. For example, the numbers 1 and 2 are consecutive. 4 and 5 are consecutive, etc

If the given numbers are same, then their Least Common Multiple (LCM) is that same number.

EXAMPLE: Find Least Common Multiple (LCM) of 5 and 5.

SOLUTION:

5 and 5 are same. 

So, Least Common Multiple (LCM) of 5 and 5 is 5.

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