HCF: Highest Common Factor LCM: Least Common Multiple

1. HCF Vs LCM
By MANIK

2. Middle Class
Student
Try to save
money
via sharing
High Class
Student
Try to spend
money
consciously
S
H
O
P
P
I
N
G
HARISH LOVISH
HCF LCM

3. Both wants to buy Two types of Chocolates
Both chocolates are available online but with different quantity per box.

4. Mindset of Both: Harish and Lovish
HARISH
• Just wants to purchase both
types of chocolates.
• Has plans to share equally
among his friends.
• The more friends, the less
spending per each.
LOVISH
• Wants to purchase both types
of chocolates but of equal
quantity.
• Has plans to buy multiple sets
of both types of chocolates.
• Minimum number of each set,
still equal quantity of both
types of chocolates in total.

5. Harish orders the chocolates and starts planning about how
many friends he can share both types of chocolates equally.
Scenario 0: One person (himself)

6. Harish orders the chocolates and starts planning about how
many friends he can share both types of chocolates equally.
Scenario 1: Among two friends (including him)

7. Harish orders the chocolates and starts planning about how
many friends he can share both types of chocolates equally.
Scenario 2: Among three friends (including him)

8. Harish orders the chocolates and starts planning about how
many friends he can share both types of chocolates equally.
Scenario 3: Among four friends (including him)

9. Possible number of friends among which
chocolate can be shared equally.
• Type I (08): 1, 2, 4, 8
• Type II (12): 1, 2, 3, 4, 6, 12
• 4 is the highest number of friends among which Harish could
divide each type of chocolates equally (including himself).
• HCF (8, 12) = 4
• HCF: Highest Common Factor

10. FAQs:
• Will Scenario 4, 5, 6 , 7, … work for Harish ?
• Can Harish share both types of chocolates equally among more
than 4 friends (including him) ?
• To conclude Harish’s arc, tell me maximum number of persons
among which 8 chocolates of Type I and 12 chocolates of Type II
could be shared equally ?
• Is he increasing or decreasing number of chocolates for him ?
• What is the maximum number of persons among which 18
chocolates of Type I and 24 chocolates of Type II could be shared
equally ?

11. Lovish orders the chocolates and starts planning about no. of
sets he needs, to get both types of chocolates equal in total.
Scenario 0: One set of each type.

12. Lovish orders the chocolates and starts planning about no. of
sets he needs, to get both types of chocolates equal in total.
Scenario 1: 1 set of Type I and 2 sets of Type II.

13. Lovish orders the chocolates and starts planning about no. of
sets he needs, to get both types of chocolates equal in total.
Scenario 2: 2 sets of Type I and 2 sets of Type II.

14. Lovish orders the chocolates and starts planning about no. of
sets he needs, to get both types of chocolates equal in total.
Scenario 3: 2 sets of Type I and 3 sets of Type II.

15. Possible number of chocolates of each type
to get equal amount in total.
• Type I (08): 8, 16, 24, 32
• Type II (12): 12, 24, 36, 48
• 24 is the lowest number of chocolates Lovish could get as equal
amount in total for each type of sets, after ordering their multiple sets.
• LCM (8, 12) = 24
• LCM: Least Common Multiple

16. FAQs:
• Do we need to go for further Scenarios for Lovish i.e. 4, 5, 6 , 7, … ?
• Can Lovish get both types of chocolates individually equal in total
for less than 24 chocolates ?
• To conclude Lovish’s arc, tell me minimum number of chocolates
(in total) he could have of each type, after ordering multiple sets of
Type I (8 chocolates in each) and Type II (12 chocolates in each) ?
• Is he increasing or decreasing number of chocolates for him ?
• What is the minimum number of chocolates (in total) he could
have of each type, after ordering multiple sets of Type I (18
chocolates in each) and Type II (24 chocolates in each) ?

17. Thanks for watching