### Challenge: Shortcut to find LCM...

Jennifer thinks there is a shortcut to find out lowest common multiple (LCM) of 2 numbers.

She says that,
"If you multiple the two numbers, you will ALWAYS get the LCM."
Is Jennifer right?

Does her method work every time? Sometimes? Never?

Explain your reasoning.
Illustrate your reasoning with examples.

Source: http://ims.ode.state.oh.us/

#### 14 comments:

1. Sometimes.
The LCM can be lesser because the two numbers a common factor other than 1.

Example: 60 and 21...
60 X 21 is 1260 but its LCM is actually 420.

2. This only works sometimes.But one thing can be for sure is that this number obtained from multiplying the two numbers IS a Common Multiple, but might not always be the Lowest.

Example: 2*6=12 but its LCM is actually 6.12 is still a Common Multiple,but not the Lowest yet.

3. This comment has been removed by the author.

4. This method works only when both of the numbers are prime numbers

Example:
2*17=34 so LCM is 34
3*19=57 so LCM is 57

5. This method only works some of the time.
Like Owen has said, for example, 25 and 50.
25*50=1250, but their LCM is actually just 100.

6. This method does not always work. It will only if both numbers are prime numbers and for some other numbers only.

Eg. 4 x 6 = 24 but their LCM is 12.

7. This method only works some of the time. If the numbers are too big, it will not work. It will only work for prime numbers.

Eg. 1st case LCM of 2 and 4. Using Jennifer's method. 2 x 4 = 8 but their LCM is actually 4.

Eg. 2nd case LCM of 2 and 3. Using Jennifer's method again. 2 x 3 = 6 their LCM is 6.

8. Sometimes only,the number will be a multiple of the two numbers, but it may not be the samllest, if the numbers are too big EG.120,300.
EG.2X3=6 the correct answer is also 6
EG.120x300=36000 the correct answer should be:600

9. I think only sometimes. I think you can get one of the multiples of the two numbers but sometimes it is not the lowest. Like 12 and 24, the LCM is not 12x24.

10. Her method only works sometimes when both numbers are prime numbers or one of the numbers is a prime number.This method works for the L.C.M of two prime numbers because the prime factors of the numbers are the same as its original number.
Example: Find the L.C.M. of 5 and 17.

Solution the index notation: 5= 5 17=17

LCM= 5X17
= 85 ( answer)
When you multiple the prime factors of the numbers you will still be multiplying the same original numbers so the answer derived is the same.Thus, this method is workable for the LCM of both prime numbers.

Jennifer's method can work for a pair of numbers when one of them is a prime number.

Example 2 : Find the LCM of number 17 and 30.

Solution (index notation) : 17=17 30=2X3X5

L.C.M= 17X2X3X5
= 510 (answer)

When you find the LCM of both the numbers, you are actually multiplying both numbers in the question.
17X2X3X5---(2X3X5) is equal to 30 which is one of the number in the question and 17 is the other number.

Example 3: Find the LCM of 6 and 16.

Solution : 6= 2X3 16=2^4

LCM= 2^4X3
= 48 ( answer)
The LCM of 6 and 16 is not the answer of 6X16= 96.

11. Jennifer's method will not work if the two numbers have common factors greater than 1.

Eg. 3x15=45 LCM of 3&15=15
Eg. 6x9=54 LCM of 6&9=18

12. Sometimes. It only works when one of the numbers is a prime number and their common factor is not more than one.

examples: work-17x2=34(LCM)
not work-33x3=99(66 is LCM)

13. ANoymous is me. Sorry.

14. Abhimanyu Arora 5/10/2011 07:30:00 PM

Sometimes. It works when at least one of the number is a prime number and their common factor is only 1.
For e.g. 5*10=50, will not work as their common factors are 1 and 5. (LCM 10)
e.g. 3*10=30, will work as one is prime number and only common factor is 1. (LCM 30)