Understand the Question For any two positive integers and , the product of their HCF and LCM equals the product of the two numbers: Rearranging to find LCM: Given , , and . Step 1 · Calculate LCM using the HCF-LCM Relationship Given numbers are and , with . Using the relation: Answer > Common Mistakes Formula Restriction: The formula holds only for two numbers, not for three or more numbers. Calculation Pitfall: Multiplying first increases the chance of arithmetic errors. Canceling common factors first (e.g. , then ) makes the calculation simpler.

Real Numbers | Exercise 1.1

Question 4

Given that $\text{HCF}(306, 657) = 9$ , find $\text{LCM}(306, 657)$ .

Solution

Understand the Question

For any two positive integers $a$ and $b$ , the product of their HCF and LCM equals the product of the two numbers: $\text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b$
Rearranging to find LCM: $\text{LCM}(a, b) = \dfrac{a \times b}{\text{HCF}(a, b)}$
Given $a = 306$ , $b = 657$ , and $\text{HCF}(306, 657) = 9$ .

Step 1 · Calculate LCM using the HCF-LCM Relationship

Given numbers are $a = 306$ and $b = 657$ , with $\text{HCF}(306, 657) = 9$ .

Using the relation: $\text{LCM}(a, b) \times \text{HCF}(a, b) = a \times b$

$\text{LCM}(306, 657) = \dfrac{\text{Product of the two numbers}}{\text{HCF}}$

$\text{LCM}(306, 657) = \dfrac{306 \times 657}{9}$

$\text{LCM}(306, 657) = \dfrac{201042}{9}$

$\text{LCM}(306, 657) = 22338$

Answer

$22338$

Common Mistakes

Formula Restriction: The formula $\text{HCF} \times \text{LCM} = a \times b$ holds only for two numbers, not for three or more numbers.
Calculation Pitfall: Multiplying $306 \times 657 = 201042$ first increases the chance of arithmetic errors. Canceling common factors first (e.g. $\dfrac{306}{9} = 34$ , then $34 \times 657 = 22338$ ) makes the calculation simpler.

Question 4

More questions in Exercise 1.1