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

ANSWERS:

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!

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7 Responses to “How to Find the LCM – FAST!!!”

  1. ronnybd says:

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

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  2. Varnika says:

    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

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  3. praveen says:

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

    6,9,7

    6,9,17,8
    ?

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    • joshturtle says:

      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!

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      • Abi Pleitez says:

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

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        • Josh Rappaport says:

          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

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  4. Woobee says:

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

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