Question

The sum of two numbers is 40. If one number exceeds another number by 10, then the Least Common Multiple of these two numbers is

• A. 75
• B. 60
• C. 80
• D. 125

Answer 1

The Correct Option is A

Let the two numbers be \( x \) and \( x + 10 \), as one number exceeds the other by 10. 
The sum of the numbers is 40: \[ x + (x + 10) = 40 \quad \Rightarrow \quad 2x + 10 = 40 \quad \Rightarrow \quad 2x = 30 \quad \Rightarrow \quad x = 15 \] The two numbers are 15 and 25. To find the LCM of 15 and 25, we use the prime factorization method: \[ 15 = 3 \times 5, \quad 25 = 5 \times 5 \] The LCM is the product of the highest powers of all prime factors: \[ LCM = 3 \times 5^2 = 75 \] To find the LCM, use the prime factorization of the numbers and take the highest powers of all primes.