SOLUTION: what is the smallest number that is divisible by 585 nd 624 ?

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Question 972502: what is the smallest number that is divisible by 585 nd 624 ?
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20855)   (Show Source): You can put this solution on YOUR website!
recall:
Least Common Multiple - The smallest number that is divisible by two or more given numbers.
so, find
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=>
and
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=>

so, the smallest number that is divisible by and is




Answer by Edwin McCravy(20083)   (Show Source): You can put this solution on YOUR website!
That's called "the least common multiple"or lcm(585,624).
We write the prime factorization of each:

Look at prime factor 2:

585 = 3*3*5*13
624 = 2*2*2*2*3*13

2 is a factor of 585 0 times.
2 is a factor of 624 4 times.

So 2 is a factor of lcm(585,624) 4 times because 4 ≥ 0.
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Look at prime factor 3:

585 = 3*3*5*13
624 = 2*2*2*2*3*13

3 is a factor of 585 2 times.
3 is a factor of 585 1 time.

So 3 is a factor of lcm(585,624) 2 times because 2 ≥ 1.
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Look at prime factor 5:

585 = 3*3*5*13
624 = 2*2*2*2*3*13

5 is a factor of 585 1 time.
5 is a factor of 585 0 times.

So 5 is a factor of lcm(585,624) 1 time because 1 ≥ 0.
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Look at prime factor 13:

585 = 3*3*5*13
624 = 2*2*2*2*3*13

13 is a factor of 585 1 time.
13 is a factor of 585 1 time.

So 13 is a factor of lcm(585,624) 1 time because 1 ≥ 1.
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Put it all together:

 2 is a factor of lcm(585,624) 4 times. 
 3 is a factor of lcm(585,624) 2 times.
 5 is a factor of lcm(585,624) 1 time.
13 is a factor of lcm(585,624) 1 time.

So lcm(585,624) = 2*2*2*2*3*3*5*13 = 9360. 

Edwin
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