For any two positive integers a and b, HCF(a, b) × LCM(a, b) = a × b. Substituting a = 96, b = 404, and HCF = 4, we find LCM(96, 404) = (96 × 404)/(4) = 24 × 404 = 9696.

Hcf or 867 and 255 find HCF and LCM of 96 and 404

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

Step-by-step solution

Step 1: Find the prime factorisation of the numbers

By applying the Fundamental Theorem of Arithmetic, we write both integers as products of their prime factors. Factoring $96$ gives $2^5 \times 3$ , and factoring $404$ gives $2^2 \times 101$ .

Step 2: Calculate 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 is $2$ , and its smallest exponent is $2$ , giving $\text{HCF} = 2^2 = 4$ .

Step 3: Calculate the LCM using the relationship formula

For any two positive integers $a$ and $b$ , $\text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b$ . Substituting $a = 96$ , $b = 404$ , and $\text{HCF} = 4$ , we find $\text{LCM}(96, 404) = \frac{96 \times 404}{4} = 24 \times 404 = 9696$ .

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