SOLUTION: how do you work out the lcm of two numbers what is the lcm of 32 and 14

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Question 825146: how do you work out the lcm of two numbers
what is the lcm of 32 and 14
Found 2 solutions by math-vortex, josgarithmetic:
Answer by math-vortex(648)   (Show Source): You can put this solution on YOUR website!
Hi, there--

Problem:
Find the least common multiple (lcm) of 32 and 14

Solution:
The least common multiple, or LCM, is a number that's useful in solving many math problems. 
One way to find the least common multiple of two numbers is to first list the prime factors of 
each number.

32 = 2 × 2 × 2 × 2 × 2 
14 = 2 × 7

Then multiply each factor the greatest number of times it occurs in either number. If the same 
factor occurs more than once in both numbers, you multiply the factor the greatest number of 
times it occurs.

Then multiply each factor the greatest number of times it occurs in either number. If the same 
factor occurs more than once in both numbers, you multiply the factor the greatest number of 
times it occurs.

2: five occurrences
7: one occurrences 

2 × 2 × 2 × 2 × 2 × 7 = 224 <— LCM

After you've calculated a least common multiple, always check to be sure your answer can be 
divided evenly by both numbers.

224 / 32 = 7
224 / 14 = 16

That's It.

Hope this helps!
Mrs. Figgy


Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
LCM, Lowest Common Multiple.

Just make several of the first whole number multiples of each number and look for the first multiple or product which occurs for both of the given numbers.

___________14______________32
2__________28______________64
3__________42______________96
4__________56______________128
5__________70______________160
6__________84______________192
7__________98______________224
.
.
Still not done...
Want better way?
Factor each given starter number into its prime factorization.
;
.

The LCM you want is the number which has the highest count of each of the involved prime factors of each given number. The 7 occurs 1 time; the 2 occurs 5 times. The lowest common multiple for 14 and 32 is .

Obviously found was , but you can examine this factorization to see how 14 is used as one of the factors to get 224 as product: ; you see already how one-by-one separate multiplications can consume so much time.
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