LCM: when calculating, is there a better method than...?

John Whitaker

Junior Member
Joined
May 9, 2006
Messages
89
When calculating the LCM of two numbers like 13 & 32, (ans. 416), is there a shortcut method of reaching this answer without creating two long lists of numbers like
13, 26, 39, 52... and 32, 64, 96, 128... all the way to 416? Thank you.
 

galactus

Super Moderator
Staff member
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Sep 28, 2005
Messages
7,216
Re: LCM

Yes, there is. Use their factorizations.

\(\displaystyle 13=13\)

\(\displaystyle 32=2^{5}\)

Now, use the largest of each. Sinc there are only two, \(\displaystyle 13\cdot{2^{5}}=416\)
 

Loren

Senior Member
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Aug 28, 2007
Messages
1,299
Re: LCM

Example:
Find the LCM of 6,8,12 and 18.

Factor each and express in exponential form.

6 = 2*3
8 = 2^3
12 = 2^2*3
18 = 2*3^2

To get the LCM select each base with its largest exponent and multiply them together.

LCM is (2^3)(3^2) = 8*9 = 72.
 

John Whitaker

Junior Member
Joined
May 9, 2006
Messages
89
Re: LCM

Thank you. Got it.
 
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