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How to calculate HCF and LCM

Updated: Aug 5, 2023


GCSE Exam style questions of HCF and LCM
How to find HCF and LCM

How to calculate HCF and LCM


Step 1: Start with the first number, 528. We'll find its prime factors.


Step 2: Begin by dividing 528 by the smallest prime number, which is 2:

528 ÷ 2 = 264


Step 3: We continue dividing by 2 until we can no longer divide evenly:

264 ÷ 2 = 132

132 ÷ 2 = 66


Step 4: Now, we move on to the next prime number, 3, and check if it divides evenly into the remaining quotient (66):

66 ÷ 3 = 22


Step 5: Next, we try dividing by 2:

22 ÷ 2 = 11


Step 6: The remaining number, 11, is a prime number. Since we cannot divide it any further, we stop here.

How to solve HCF and LCM
HCF and LCM

Step 1: Begin by dividing 248 by 2:

248 ÷ 2 = 124


Step 2: Continue dividing by 2:

124 ÷ 2 = 62


Step 3: Divide by 2 again:

62 ÷ 2 = 31


Since 31 is a prime number, we stop here.


Now you need to follow the steps of Venn Diagram below;

How to use venn diagram to find HCF and LCM
HCF and LCM using venn diagram

Step 1: Create two circles within a rectangle, representing the two numbers.


Step 2: Write the prime factors of the first number (528) in the left circle. In this case, the prime factors are 2, 2, 2, 3, and 11.


Step 3: Write the prime factors of the second number (248) in the right circle. The prime factors for 248 are 2, 2, 2, and 31.


Step 4: Place the common prime factors in the overlapping region of the two circles. The common prime factors in this case are 2, 2, and 2.


Step 5: Multiply the common prime factors together to find the HCF. The HCF is 2 × 2 × 2, which is equal to 8.

How to find HCF and LCM
Venn diagram to find HCF and LCM

Step 6: Write the remaining prime factors. For 528, the remaining prime factors are 2, 3 and 11.

For 248, the remaining prime factor is 31.


Step 7: Multiply all the prime factors in the Venn diagram together, including those in the overlapping region to find the LCM.


In this case, the LCM is 2 × 2 × 2 × 2 x 3 × 11 × 31, which is equal to 16,368.


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