## Where math comes alive

### How to Find the LCM – FAST!!!

Ever need to find the LCM (same as the LCD) for a pair of two numbers, but you don’t feel like spending two hours writing out the multiples for the numbers and waiting till you get a match.

Of course you need to do this — a lot!  Example:  whenever you add fractions with different denominators you need to find the common denominator. That is the LCM.

Here’s a quick way to do this.

The only way to teach this is by example, so that’s what I’ll do — by finding the LCM for 18 and 30.

Step 1)  Find the GCF for the two numbers.

For 18 and 30, GCF is 6.

Step 2)  Divide that GCF into either number; it doesn’t matter which one you choose, so choose the one that’s easier to divide.

Choose 18. Divide 18 by 6. Answer = 3.

Step 3)  Take that answer and multiply it by the other number.

3 x 30  =  90

Step 4)  Celebrate …

… because the answer you just got is the LCM. It’s that easy.

Note:  if you want to check that this technique does work, divide by the other number, and see if you don’t get the same answer.

PRACTICE:  Find the LCM (aka LCD) for each pair of numbers.

a)  8 and 12
b)  10 and 15
c)   14 and 20
d)  18 and 24
e)  18 and 27
f)  15 and 25
g)  21 and 28
h)   20 and 26
j)   24 and 30
k)  30 and 45
l)  48 and 60

a)  8 and 12; LCM =  24
b)  10 and 15; LCM =  30
c)   14 and 20; LCM =  140
d)  18 and 24; LCM =  72
e)  18 and 27; LCM =  54
f)  15 and 25; LCM =  75
g)  21 and 28; LCM =  84
h)   20 and 26; LCM =  260
j)   24 and 30; LCM =  120
k)  30 and 45; LCM =  90
l)  48 and 60; LCM =  240

Once you learn this trick, have fun using it, as it is a real time-saver!

#### Comments on: "How to Find the LCM – FAST!!!" (36)

1. ronnybd said:

THNX, you can’t blv how mch time this sves! <3

2. Varnika said:

Hi. Nice trick, will be very helpful for competitions. But what if there are more than two numbers or a bigger number like for example 3190 or any may be any other number.

Would this trick help in solving such problems?

Regards

3. praveen said:

but how to find it for greater than 2 numbers
like for
4,6,8

6,9,7

6,9,17,8
?

• Praveen,

The easiest way to find the LCM for two or more numbers is this.

First, prime factorize the three numbers.

Secondly, line up the prime factors.

Thirdly, for each prime number, choose the largest factor. Call these the “LCM factors.”

Fourthly, multiply the LCM factors together. The product will be the LCM of the various numbers.

Example, find the LCM for 12, 15, 24

Prime Factorizations:

12 = 2^2 x 3
15 = 3 x 5
24 = 2^3 x 3

LCM factors:
for 2, it is 2^3 = 8
for 3, it is 3^1 = 3
for 5, it is 5^1 = 5

Product of LCM factors: 8 x 3 x 5 = 120
So the LCM for the three numbers = 120

Hope that helps!

• i cant find the lcm of 11 and 13 i think ill leave that way cuz i couldnt find it

• Hello,

The LCM for 11 and 13 is extremely easy to find, so you don’t need any kind of trick for it.
When looking for the LCM of two numbers, both of which are prime, you find it simply
by multiplying the two numbers together. So the LCM for 11 and 13 is just 143 (11 x 13) since both
11 and 13 are prime.

In fact, the trick I just explained works in a broader sense. Whenever the larger of
the two numbers is prime, you just multiply the two numbers together to find
the LCM. So for example, you would just multiply the two numbers to find
the LCM for:

a) 12 and 17
b) 16 and 31
c) 24 and 37

since for each pair, the larger number (17, 31, 37) is
prime.

Hope that helps!
—  Josh

• Jonathan said:

Hey Josh,

Thank you SO MUCH for the tips and tricks. I find it a HUGE time saver when solving mathematics by hand. My professor insists I solve using the original method, but I believe anyone would prefer a short cut to a problem that will get them the exact same result. Now if you can just figure out a short cut to become wealthy…

Cheers,

Jon

4. lola said:

thank you sooooooooo much I like it! you just make my day.

5. Woobee said:

Wow, this is extremely helpful! Thank you! I discovered this trick by myself, but I forgot it. :/ Once again, thank you!

6. debbie said:

find 2 numbers so that 30 is the lowest common multiple of the two numbers, neither of the numbers maybe 30.
i would be really greatful for info

• Hi Debbie,

How about 15 and 6? Or 15 and 10? Or 10 and 6. Hope that helps. — Josh

7. Ts. said:

Yo, this trick has really helped a lot. Thank-you. Just wanted to ask if you know of any other easy tricks to do conversion problems? Also, as you said ‘if the larger number of the two is a prime number you multiple the two together’ does that ALWAYS work?

Regards. x

• To answer your last question first, yes, this is always true. If you’re finding the LCM for any two numbers, and the larger number is prime, you ALWAYS find the LCM by just multiplying the two numbers together. To answer your previous question, here’s another trick. If you’re finding the LCM for two numbers, and those numbers have NO COMMON FACTORS — like 4 and 15; or 9 and 25 — again you get the LCM by just multiplying the two numbers together. The reason is that two numbers have an LCM that’s less than their product ONLY IF THEY HAVE A COMMON FACTOR.

8. Wow! thanks so much for your tip. I’m having a little trouble following your advice about finding the LCM for more than 3 numbers. I saw it above but I got lost after finding the prime factorizations. Could you help?

9. Hi Gabriella,

I don’t know what else I can tell you, other than what I said in my post. You prime factorize all of the numbers. Then for each prime factor, you take the factor with the largest exponent. For example, if you have factors of X^3, x^5 and x^4, you would use the x^5 factor, since 5 is the largest of the three exponents: 3, 4 and 5. Then, once you have those factors, you just multiply them together to get the LCM. If you are still puzzled by this, perhaps it would help if you share a specific problem for which you are unsure how to find the LCM.

• Gabriella said:

Thanks so much for the clarification and the great site, Josh.

10. This stuff is really awesome
at first i wad just looking for a site that would tell me the answer but its so cool how u actualy explaimed everything josh.
so i just wanted to say good job

11. itz amazing

12. vins said:

thanx

13. it’s great…:D

14. Yanna Bannana said:

COOL!:D thanks i got perfecto in our long test, great work!!

15. [...] The information in this video dovetails with the info in this post. [...]

16. what is the lcm of 72 and 120???

• GCF of 72 & 120 = 24
72 ÷ 24 = 3
3 x 120 = 360

LCM = 360

• Abby said:

can you show us how to do this with not 1, not 2, but 3 numbers!!!!! i know that you can do it, wiz kid ( no really, this homework is killing me dude)

17. Wow that was strange. I just wrote an extremely long comment but after I
clicked submit my comment didn’t show up. Grrrr… well I’m not writing all that over again.
Anyway, just wanted to say fantastic blog!

18. Rainbow Dash ⚡ said:

Thanx a lot! Your tips really helped! 😀

19. James said:

Awesome! You just helped me work this out, now I can sleep!

21. Vishesh said:

Hey josh
Great site. Thanks a lot. Solved a lot of problems.
I have one request. Can you show easier way to find GCF too.
Thanks

22. It’s not my first time to pay a quick visit this web site, i am visiting this web site dailly and get pleasant data from here everyday.

23. thank you very much you help me in my math test

24. Simara said:

Can you please solve this 48 and 60; LCM = 240? because my answer was 480, so do we always need to simplify the answer?

• Hi Simara,
The correct answer is 240. With my technique, you use the GCF, which is 12. 12 goes into 48 4 times. Take that answer, 4, and multiply it by the other number, 60. 4 x 60 = 240, and that is the LCM. You can check it and see. 48 goes into 240 5 times. And 60 goes into 240 4 times. And there’s no number smaller than 240 that both 48 and 60 go into. So that’s it.