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 between two numbers check first if the smaller of the two numbers can be divided into the larger one without leaving a remainder. If not multiply the larger number by 2 and ask the same question. Keep incrementing the multiplier and do the same process until the smaller number can be wholly divided into the larger number’s multiples.

For example, finding the lowest common multiple between 4 and 10 would look like this in a step-by-step approach:

- Does 4 divide into 10 without leaving a remainder? No, as it goes 2 times with a remainder of 2.
- 10 times 2 is 20.
- Does 4 divide into 20 without leaving a remainder? Yes, 4 goes 5 times with no remainder.

Once the smaller number wholly goes into the multiple of the larger number then you’ve found the lowest common multiple between both numbers.

In the example with the numbers of 4 and 10 the lowest common multiple would be 20.

## How To Check Your Answer

If you want to check your answer simply divide each number by the lowest common multiple (LCM).

Once you have the multiple for the larger number start counting down to 1 at each count down multiplying that number to the larger number and checking if the smaller number can be divided without remainder into the new multiple.

For example, with the answer of 20 I would divide this by 10 which would give me 2. Decrementing the number down by subtracting 1 would leave me with 1. 10 times 1 is 10, and dividing 4 into 10 would leave me with a remainder therefore I can be confident that the lowest common multiple of 4 and 10 is 20.

## Is There A Faster Way To Find LCM?

Sometimes multiplying both numbers together can produce the lowest common multiple between two numbers.

For example, mutiplying the numbers 4 and 10 together would produce the multiple 40. While this is a
**
common multiple,
**
it is not the
**
**
*
lowest
*
**
common multiple.
**

To find the lowest common multiple using this “short-cut” technique would mean going through the check process above.

- 10 divided into 40 is 4.
- 4 subtract 1 is 3.
- 10 times 3 is 30.
- Can 4 be divided into 30 without remainder? No, it has a remainder of 2.
- 3 subtract 1 is 2.
- 10 times 2 is 20.
- Can 4 be divided into 20 without remainder? Yes!
- 2 subtract 1 is 1.
- 10 times 1 is 10.
- Can 4 be divided into 10 without remainder? No, it has 2 remainder.

From the above check the answer would be 20.

But is this method really a “short-cut”? I don’t think so.

## Summary

The lowest common multiple between 10 and 4 is 20.

The fastest process in finding the lowest common multiple is to multiply the larger number by 1 and to see if the smaller number can be divided into the larger multiple. If it can you have the lowest common multiple. If not increment the multiplier (2, 3, 4… etc) and repeat the process.