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InsightfulPenguin3718

Hello ! I do not know when to apply the LCM and GCF. Can you help me? 

Sarah G

Hello,

As it is known, LCM stands for Least Common Multiple and GCF stands for Greatest Common Factor.

We use the LCM when we have to find the smallest positive multiple common to ALL the numbers we are dealing with. A common example where using the LCM is useful is when you have multiple fractions and wish to transform them in order to all have the same denominator.

As an example, let us calculate the LCM of 3 and 4. We will list the multiples of 3: 3 - 6 - 9 - 12 - 15 - 18 - 21 - 24 - 27 - 30 - 33 - 36 - 39 - 42-48 etc…

and the multiples of 4: 4 - 8 - 12 - 16 - 20 - 24 - 28 - 32 - 36 - 40 - 44 - 48 - 52 etc…

It is then a matter of looking at the common numbers and taking the smallest of these multiples.

In this case, only 12, 24 and 48 are numbers in common to both 3 and 4. The smallest is 12, therefore, it is the LCM! In other words, the LCM or the least common multiple to 3 and 4 is 12.

In another order of ideas, we use the GCF when we are working with a set of numbers, and wish to find the largest common number that divides evenly into each number in this given set.

For example, 24 and 16 are both divisible by 2, therefore, 2 is a common divisor of 24 and 16. However, 24 and 16 are also divisible by 4 and by 8. The GCD is simply the biggest of all these common dividers: 8. 

Hope I was able to help you! 

See you next time :)

Laura A

Hi there !

Thank you for your question today ! As you may know, LCM stands for lowest common multiple and GCF for greatest common factor, and I think I have the link for you. Check it out:

https://www.purplemath.com/modules/lcm_gcf.htm

If it still isn't as clear as you would like it to be, please feel free reaching out anew : )