Question 4 of 10beginner🔧 ApplyNumerical2 marks

Given that HCF(306, 657) = 9, find LCM(306, 657).

Correct Answer

Given: HCF(306, 657) = 9

Formula: HCF × LCM = Product of the two numbers

Solution: HCF(306, 657) × LCM(306, 657) = 306×657306 \times 657

9 × LCM(306, 657) = 201042

LCM(306, 657) = 201042 ÷ 9

LCM(306, 657) = 22338

Answer: LCM(306, 657) = 22338

Exercise: Exercise 1.1 | Q: 4 | (Page Page 5)
For More Understanding

Explanation

For any two positive integers a and b, the relationship HCF(a,b) × LCM(a,b) = a × b holds. This allows us to find LCM when HCF is known, or vice versa. Here, we use this relationship to find LCM(306, 657) given that HCF(306, 657) = 9.

Solution Steps

  1. Step 1: Use the formula HCF × LCM = Product of two numbers

  2. Step 2: Substitute given values: 9 × LCM = 306×657306 \times 657

  3. Step 3: Calculate: 9 × LCM = 201042

  4. Step 4: Solve for LCM: LCM = 201042 ÷ 9 = 22338

PreviousNext