We are given that HCF = 12, LCM = 420, and one number a = 60. Let the required second number be b.

Substituting the given values into the relationship HCF × LCM = a × b, we obtain 12 × 420 = 60 × b.

if the HCF of two numbers is 12 and the LCM is 420 and one number is 60 find the other number

Answer: 84

Step-by-step solution

Step 1: State the relationship between HCF, LCM, and two numbers

For any two positive integers $a$ and $b$ , the product of their highest common factor and least common multiple equals the product of the two numbers itself.

Step 2: Identify the given values

We are given that $\text{HCF} = 12$ , $\text{LCM} = 420$ , and one number $a = 60$ . Let the required second number be $b$ .

Step 3: Substitute the values into the formula

Substituting the given values into the relationship $\text{HCF} \times \text{LCM} = a \times b$ , we obtain $12 \times 420 = 60 \times b$ .

Step 4: Solve for the unknown number

Dividing $420$ by $60$ gives $7$ . Multiplying $12$ by $7$ gives $84$ . Thus, the other number is $84$ .

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