Multiple choice

There are 5 consecutive natural numbers with LCM 60. The product of the first two numbers is equal to the 5th number. What is the sum of the numbers?

  1. 15

  2. 16

  3. 18

  4. 20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the numbers be x, x+1, x+2, x+3, x+4. LCM(x, x+1, x+2, x+3, x+4) = 60. Testing consecutive integers, 2, 3, 4, 5, 6 gives LCM 60. Product of first two is 2 * 3 = 6, which is the 5th number. Sum = 2+3+4+5+6 = 20.

AI explanation

Let the 5 consecutive natural numbers be x, x+1, x+2, x+3, and x+4. Testing the smallest natural numbers, the set starting with 1 has a product of the first two numbers equal to 1, which is not the fifth number; however, the set starting with 2 gives 2 times 3 equaling 6, which perfectly matches the fifth number. The least common multiple of 2, 3, 4, 5, and 6 is 60, verifying all conditions. Adding these five numbers (2 + 3 + 4 + 5 + 6) gives a sum of 20.

Keep practicing — related questions