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If the least common multiple (LCM) of two numbers is 60 and their greatest commo

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Question: If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 5, which of the following pairs could represent these two numbers?

Options:

  1. (5, 12)
  2. (10, 30)
  3. (15, 20)
  4. (5, 15)

Correct Answer: (15, 20)

Solution: 

The product of the two numbers is equal to the LCM multiplied by the GCD. Thus, 60 * 5 = 300. The pair (15, 20) satisfies this condition since 15 * 20 = 300.

If the least common multiple (LCM) of two numbers is 60 and their greatest commo

Practice Questions

Q1
If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 5, which of the following pairs could represent these two numbers?
  1. (5, 12)
  2. (10, 30)
  3. (15, 20)
  4. (5, 15)

Questions & Step-by-Step Solutions

If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 5, which of the following pairs could represent these two numbers?
  • Step 1: Understand the problem. We need to find two numbers that have a least common multiple (LCM) of 60 and a greatest common divisor (GCD) of 5.
  • Step 2: Recall the relationship between LCM, GCD, and the product of two numbers. The formula is: Product of the two numbers = LCM * GCD.
  • Step 3: Calculate the product of the two numbers using the given LCM and GCD. Here, LCM is 60 and GCD is 5. So, we calculate: 60 * 5 = 300.
  • Step 4: Now we know that the product of the two numbers must equal 300. We need to find pairs of numbers that multiply to 300.
  • Step 5: Check the pair (15, 20). Calculate 15 * 20. It equals 300, which is correct.
  • Step 6: Verify that the LCM of 15 and 20 is 60 and the GCD is 5. The GCD of 15 and 20 is indeed 5, and the LCM is 60.
  • Step 7: Conclude that the pair (15, 20) satisfies both conditions of LCM and GCD.
  • Least Common Multiple (LCM) – The smallest multiple that is exactly divisible by two or more numbers.
  • Greatest Common Divisor (GCD) – The largest positive integer that divides two or more numbers without leaving a remainder.
  • Relationship between LCM and GCD – The product of two numbers is equal to the product of their LCM and GCD.
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