Question

What is the lowest common multiple of $5,7$ and $10$?

Answer 1

To find the LCM (Lowest common multiple) of a set of numbers, you first find the multiples of each number and then identify the smallest common one among the set.
In this case, using $5,7$, and $10$. The smallest common multiple of each would be $70$. If we find the multiples of each of the numbers, we can see that no other number before $70$ is common to all of them.
Multiples of $5:5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,...$
Multiples of $7:7,14,21,28,35,42,49,56,63,70,77,...$
Multiples of $10:10,20,30,40,50,60,70,80,...$
If you realize, the only common multiple up to this point is $70$. There may be other common multiples but you are looking for the smallest (or lowest) one.
Note: The way you find multiples is to multiply the number you are trying to find numbers for by each number in succession.
For example, multiples of $3:3(3\cdot 1),6(3\cdot 2),9(3\cdot 3),12(3\cdot 4),15(3\cdot 5),...$.