Lowest common multiple

[bt2005]

Hello, could someone show me the method to calculator the lowest common multiple of 92, 104 and 123.

Thank you!

 

[pka]

Hello, could someone show me the method to calculator the lowest common multiple of 92, 104 and 123.

Find the prime factorization of each: \(\displaystyle 92=2^2\cdot23,~104=2^3\cdot13,~123=3\cdot41,~\)
List each factor: \(\displaystyle 2\cdot 3\cdot 13\cdot 23\cdot 41\)
Take the greatest power \(\displaystyle 2^3\cdot 3\cdot 13\cdot 23\cdot 41=294216\) SEE HERE

 

[Dr.Peterson]

Hello, could someone show me the method to calculator the lowest common multiple of 92, 104 and 123.

There are several ways to calculate an LCM. This page describes the three best-known: https://artofproblemsolving.com/wiki/index.php/Least_common_multiple . I am aware of several other ways.

Perhaps you should choose a method (from that page or another, or from your own textbook), and show us your attempts at your problem, so we can guide you along.

 

[topsquark]

Hello, could someone show me the method to calculator the lowest common multiple of 92, 104 and 123.

Thank you!

The way I was taught was to break each number down into it's prime factors. We have
\(\displaystyle 92 = 2^2 \cdot 23\)

\(\displaystyle 104 = 2^3 \cdot 13\)

\(\displaystyle 123 = 3 \cdot 41\)

Now, for your lcm you want all of the primes to their highest order. For example you want a factor of \(\displaystyle 2^3\) and not \(\displaystyle 2^2\). So your lcm will be \(\displaystyle 2^3 \cdot 3 \cdot 13 \cdot 23 \cdot 41= 294216\).

-Dan

Addendum: Wow! Two posts while I was typing that up! I've been soundly beaten!

 

[Deleted member 4993]

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Addendum: Wow! Two posts while I was typing that up! I've been soundly beaten!

No - you have been lightly beaten... with photons (wavicles) not waves....