Method to find the smallest number with given factors

Hi :) I would like to know a way how to find the smallest number with given factors.

I have two examples that I know the answer to because I looked at the answer book so to speak, but I don't understand how to get to the answer.

The first example is : Find the lowest number whose factors are 4, 18.
The answer is 36, but what is the method to find out without me looking in the answer book?
The second example is: Find the smallest number whose factors are 2, 4 ,9.
The answer is also 36, but what is the method to find out without me looking in the answer book?

Thanks in advance, I'll try and get round to choosing a best answer this time! :F

(Just in case you are wondering... My maths book is a workbook with places to answer and an answer book rather than it specifically teaches)

Express each number as the product of its prime factors.
4 = 2 x 2
18 = 2 x 3 x 3
The lowest common multiple will be 2 x 2 x 3 x 3 = 36.

2 = 2
4 = 2 x 2
9 = 3 x 3
Again the lowest common multiple will be 2 x 2 x 3 x 3 = 36

The lowest common multiple will have all the factors of the numbers in the question and where a factor is repeated it will be repeated the same number of times in the lowest common multiple. Sorry, that's a bit hard to explain. See if this example helps.

Find the lowest common multiple of 50 and 60.
50 = 2 x 5 x 5
60 = 2 x 2 x 3 x 5
The lowest common multiple is 2 x 2 x 3 x 5 x 5 = 300

follow the steps:
1) multiply the numbers Eg-36x18=648
2) calculate the hcf of the numbers:

a)write the prime factors of both the numbers:
Eg- 36=3x3x2x2
18=2x3x3
b)pick out the common factors from both
there are two 3's and one 2 common
c)multiply them:3x3x2= 18

3)divide the product obtained in 1) by hcf:
648/18=36

this is your answer.



Or


just calculate the LCM (same thing really).

PS:you can do the same for more than 2 numbers as well. Just pick the common factors of all the three.