What is the LCM of the numbers 4, 5, and 10? 40 30 20 10
The Correct Answer and Explanation is:
Correct Answer: 20
This answer is incorrect. Let’s find the correct Least Common Multiple (LCM) of 4, 5, and 10 step-by-step and determine the accurate choice among the given options: 40, 30, 20, 10.
Step 1: Prime Factorization
- 4 = 2 × 2 = 2²
- 5 = 5 (a prime number)
- 10 = 2 × 5
To find the LCM, we take each prime factor that appears and raise it to the highest power it occurs in any of the factorizations.
- The factor 2 appears as 2² in 4
- The factor 5 appears as 5 in both 5 and 10
So, the LCM will be:
LCM = 2² × 5 = 4 × 5 = 20
Step 2: Verify
Check that 20 is divisible by all three numbers:
- 20 ÷ 4 = 5 → whole number ✅
- 20 ÷ 5 = 4 → whole number ✅
- 20 ÷ 10 = 2 → whole number ✅
Therefore, 20 is the smallest number divisible by 4, 5, and 10.
Why not the other choices?
- 10 is divisible by 5 and 10, but not by 4 ❌
- 30 is divisible by 5 and 10, but not by 4 ❌
- 40 is divisible by all three, but it is not the smallest common multiple ❌
Conclusion
The correct answer is: 20
The Least Common Multiple is a useful concept in solving problems involving synchronization of events, finding common denominators, or aligning periodic events. It ensures that we identify the smallest value shared as a multiple by different numbers, avoiding unnecessary repetition or larger values.
