1. Finding LCM (2 numbers)
- Ladder Method

2. Recap- Common Multiples
Multiples that are common to two or more numbers are said to be Common multiples.
2 and 3 Multiplication Tables
Write the Common Multiples of 2 and 3 Multiples of 2 are 2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 Multiples of 3 are 3 , 6 , 9 , 12 , 15, 18 , 21 , 24 , 27 , 30 So, common multiples of 2 and 3 are 6 , 12 , 18 , …

3. Lowest Common Multiple
Definition: The Lowest Common Multiple (LCM) of two or more given numbers
is the lowest (or smallest or least) of their common multiples.
Example: What is the Lowest Common Multiple of 2 and 3?
Multiples of 2: 2 , 4 , 6 , 8 , 10 ,12 ,…
Multiples of 3: 3 , 6 , 9 , 12 ,15 ,….
The common multiples of 2 and 3 are 6, 12 etc…..
The Lowest Common Multiple will be the lowest of their common multiples .i.e. 6.
Therefore LCM of 2 and 3 is 6.

4. LCM by Ladder Method
Step 1: Divide by a common factor of both the given numbers Step 2: Continue to divide till the only numbers left to divide is 1 and / or prime numbers Step 3: LCM is the product of all factors and the numbers left

5. LCM by Ladder Method - Variation
Step 1: Divide by a common factor of both the given numbers. If there is no common factor, LCM is the product of the given numbers.

6. Example 1: Find the LCM of 24 , 36 using ladder method
Solution:
Step 1: Divide by a common factor of both the
given numbers
Step 2: Continue to divide till the only numbers
left to divide is 1 and/ or prime numbers
Step 3: LCM is the product of all factors and the
numbers left
LCM (24, 36) = 72
Ans: 72
, 36 2
, 18
6 , 9 3
2 , 3
Only number left are 1 or/and prime numbers, so we stop here
LCM = 2 x 2 x 3 x 2 x 3 = 72

7. Example 2: Find the LCM of 12 , 36 using ladder method
Solution:
Step 1: Divide by a common factor of both the
given numbers
Step 2: Continue to divide till the only numbers
left to divide is 1 and/ or prime numbers
Step 3: LCM is the product of all factors and the
numbers left
LCM (12, 36) = 36
Ans: 36
, 36 2
6 , 18
3 , 9 3
1 , 3
Only number left are 1 or/and prime numbers, so we stop here
LCM = 2 x 2 x 3 x 1 x 3 = 36

8. 7 21 , 49 3 , 7 Example 3: Find the LCM of 21 , 49 using ladder method
Solution:
Step 1: Divide by a common factor of both the given numbers
Step 2: Continue to divide till the only numbers
left to divide is 1 and /or prime numbers
Step 2: LCM is the product of all factors and the
numbers left
LCM (21, 49) = 147
Ans: 147
, 49 7
3 , 7
Only number left are 1 or/and prime numbers, so we stop here
(in this case there is no need for this step so we stop)
LCM = 7 x 3 x 7 = 147

9. Example 4: Find the LCM of 30, 60 using ladder method
Solution:
Step 1: Divide by a common factor of both the
given numbers
Step 2: Continue to divide till the only numbers
left to divide is 1 and/ or prime numbers
Step 3: LCM is the product of all factors and the numbers left
LCM (30, 60) = 60
Ans: 60
, 60 10
3 , 6 3
1 , 2
Only number left are 1 or/and prime numbers, so we stop here
LCM = 10 x 3 x 1 x 2 = 60

10. 59 , 77 Example 5: Find the LCM of 59, 77 using ladder method
Solution:
Step 1: Divide by a common factor of
both the given numbers.
As there is no common factor LCM is the product of the given numbers
LCM (59, 77) = 4543
Ans: 4543
59 , 77
No common factor
LCM = 59 x 77 = 4543

11. Try these
1. Find the lowest common multiple of 25 and 65? 2. Find the lowest common multiple of 16 and 72? 3. Find the lowest common multiple of 70 and 80?