I'm thinking of a number.
My number is both a multiple of 5 and a multiple of 6.
What could my number be?
What else could it be?
What is the smallest number it could be?
To find any number that satisfies a number with multiples both of (for example 5 and 6), you must find the common multiple. There are infinite amounts of common multiples. Here, I will list them out -
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90.
6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96.
Here, we can see that there is a correlation. The same numbers are 30, 60 and 90.
To find the smallest common multiple (LCM), you must find the first number that has a connection. In this one: It's 30.
I'm thinking of a number.
My number is a multiple of 4, 5 and 6.
What could my number be?
What else could it be?
What is the smallest number it could be?
For this, there are 3 numbers, which makes it more difficult. But use the same method. (list them out!)
4: 4, 8, 12, 16, 20, 24, 28, 32, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120.
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120.
6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120.
Again, let us find the number that correlates with all 3 lists of the multiples - They are:
60, 120, and infinitely more.
The LCM of 4, 5 and 6 is 60. (the first occurring number)
It could be another number such as 120.