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.

**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;

**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.

**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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