We calculate the product of the HCF and LCM: 4 × 9696 = 38784. Next, we calculate the product of the two given numbers: 96 × 404 = 38784. Since both values are equal to 38784, the relationship is verified.

We calculate the product of the HCF and LCM: 4 × 9696 = 38784. Next, we calculate the product of the two given numbers: 96 × 404 = 38784. Since both values are equal to 38784, the relationship is verified.

Hcf or 867 and 255 find HCF and LCM of 96 and 4 note 4 verify the HCF and you LCM is equal to product of two numbers

Answer: $\text{HCF}(96, 404) = 4$ , $\text{LCM}(96, 404) = 9696$ , and $\text{HCF} \times \text{LCM} = 96 \times 404 = 38784$ .

Step-by-step solution

Step 1: Prime factorisation of 96 and 404

We express both numbers as products of their prime factors using exponent notation. For 96, repeated division by 2 gives 5 factors of 2 and 1 factor of 3, so $96 = 2^5 \times 3^1$ . For 404, dividing by 2 twice leaves 101, which is a prime number, giving $404 = 2^2 \times 101^1$ .

Step 2: Find the HCF

The Highest Common Factor is the product of the smallest power of each common prime factor involved in the numbers. The only common prime factor between 96 and 404 is 2, and the smallest power of 2 is $2^2 = 4$ .

Step 3: Find the LCM

The Least Common Multiple is the product of the greatest power of each prime factor involved in the numbers. We take $2^5$ , $3^1$ , and $101^1$ . Multiplying these together gives $32 \times 3 \times 101 = 9696$ .

Step 4: Verify HCF x LCM = Product of two numbers

We calculate the product of the HCF and LCM: $4 \times 9696 = 38784$ . Next, we calculate the product of the two given numbers: $96 \times 404 = 38784$ . Since both values are equal to 38784, the relationship is verified.

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