HCF (Highest Common Factor) Problems
1. Find the HCF of 8 and 12.
Hint: List out the factors of each number and find the highest number that is common to both
lists.
2. What is the highest common factor of 14 and 28?
Hint: Think about what numbers can divide both 14 and 28 without leaving a remainder.
3. Choose the correct HCF:
What is the HCF of 9 and 6?
A) 1
B) 2
C) 3
D) 6
4. Two numbers have an HCF of 5. One of the numbers is 20. What could be the other number?
A) 15
B) 25
C) 10
D) 30
Hint: Which of these numbers has 5 as a factor along with 20?
5. Solve for HCF:
Find the HCF of 16 and 24 by listing their factors.
LCM (Least Common Multiple) Problems
1. Find the LCM of 3 and 4.
Hint: List the multiples of each number until you find the smallest multiple they both share.
2. What is the least common multiple of 5 and 6?
Hint: Keep listing the multiples of 5 and 6 until you find the first one they have in common.
3. Choose the correct LCM:
What is the LCM of 7 and 8?
A) 56
B) 14
C) 21
D) 28
4. Calculate the LCM for 9 and 12.
Hint: List the multiples of 9 and 12, then find the smallest number that appears in both lists.
5. Two numbers have an LCM of 20. One of the numbers is 5. What could be the other number?
A) 2
B) 4
C) 5
D) 10
Hint: Which of these numbers when multiplied with 5 gives a product or has a common
multiple of 20?
Mixed HCF and LCM Problems
1. Rahul and Tina are trying to sync their exercise schedule. Rahul exercises every 8 days and
Tina every 12 days. If they exercised together today, after how many days will they exercise
together again?
Hint: Find the LCM of 8 and 12 to determine the next day they will both exercise.
2. Two friends are wrapping presents with ribbons. One has a ribbon 18 meters long and the
other has a ribbon 24 meters long. They want to cut the ribbon into pieces of equal length with
no ribbon left over. What is the longest length each piece can be?
Hint: Find the HCF of 18 and 24 to find the longest length of each piece.