Question 11 of 18intermediate🔧 ApplyNumerical2 marks

Find two numbers whose HCF is 1 and LCM is 66.

Correct Answer

Given: HCF = 1, LCM = 66

Formula: Product of two numbers = HCF × LCM

Calculation: Product = 1×661 \times 66 = 66

Prime factorisation: 66 = 2×32 \times 3 × 11

Finding co-prime pairs: Since HCF = 1, the numbers must be co-prime. We split the prime factors into two groups:

  • (2) and (3×113 \times 11 = 33)
  • (3) and (2×112 \times 11 = 22)
  • (2×32 \times 3 = 6) and (11)

Answer: The two numbers are 2 and 33, or 3 and 22, or 6 and 11.

Exercise: Figure it Out (Section 6) | Q: 13 | (Page Page 17)
For More Understanding

Explanation

When HCF = 1, the numbers are co-prime. The chapter establishes that HCF × LCM = product of the two numbers. So the product must be 66. We need to find two co-prime numbers that multiply to 66. The prime factorisation of 66 is 2×32 \times 3 × 11. We can split these primes into two groups: (2) and (3×113 \times 11=33), or (3) and (2×112 \times 11=22), or (2×32 \times 3=6) and (11).

Solution Steps

  1. Step 1: Since HCF = 1, the numbers are co-prime.

  2. Step 2: Product = HCF × LCM = 1×661 \times 66 = 66.

  3. Step 3: Find prime factorisation of 66 = 2×32 \times 3 × 11.

  4. Step 4: Split into co-prime pairs: (2, 33), (3, 22), or (6, 11).

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