What is the lowest common multiple of the numbers 4 and 10, and how do you arrive at the answer?

To find the lowest common multiple (LCM) between two numbers, check whether the smaller number divides evenly into a multiple of the larger number.

Start by multiplying the larger number by 1, then by 2, then by 3, and so on. At each step, test whether the smaller number divides evenly (with no remainder) into that multiple.

Example: Find the LCM of 4 and 10

  • $10 \div 4$ leaves a remainder → ❌
  • $10 \times 2 = 20$
  • $20 \div 4 = 5$ with no remainder → ✅

So, the lowest common multiple of 4 and 10 is 20.

How To Check Your Answer

You can verify your answer by checking that both original numbers divide evenly into the result.

  • $20 \div 10 = 2$
  • $20 \div 4 = 5$

Both divide cleanly with no remainder. ✅

Alternatively, you can walk backward from your result and test smaller multiples:

  • $10 \times 1 = 10 \Rightarrow 10 \div 4 = 2$ remainder → ❌
  • $10 \times 2 = 20 \Rightarrow 20 \div 4 = 5$ → ✅

So no smaller multiple than 20 works — confirming the LCM is 20.

Is There A Faster Way?

A common shortcut is to multiply both numbers together:

$$ 4 \times 10 = 40 $$

While 40 is a common multiple, it’s not the lowest common multiple.

You’d still need to check whether smaller multiples (like 30 or 20) satisfy the conditions:

  • $40 \div 10 = 4$, $40 \div 4 = 10$ ✅
  • $30 \div 10 = 3$, $30 \div 4 = 7.5$ ❌
  • $20 \div 10 = 2$, $20 \div 4 = 5$ ✅

So while multiplying the two numbers gives you a multiple, it doesn’t always give the lowest one — and often leads to more checking.

Summary

The lowest common multiple of 4 and 10 is 20.

To find the LCM:

  1. Multiply the larger number by increasing values (1, 2, 3…)
  2. Check each result to see if the smaller number divides evenly
  3. The first such result is your LCM

It’s the fastest and most reliable method.