Least Common Multiple – Find It Fast With a Trick
Ever need to find the least common multiple (known as the LCM) 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. You also need to use the LCM for algebra, when you add algebraic fractions.
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 = 9
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 2
D) 18 and 24.
E) 18 and 27.
F) 15 and 25.
G) 21 and 28.
H) 20 and 26.
J) 24 and 3
K) 30 and 45.
L) 48 and 6
A) 8 and 12; LCM = 24.
B) 10 and 15; LCM = 3
C) 14 and 20; LCM = 14
D) 18 and 24; LCM = 144.
E) 18 and 27; LCM = 54.
F) 15 and 25; LCM = 75.
G) 21 and 28; LCM = 84.
H) 20 and 26; LCM = 26
J) 24 and 30; LCM = 12
K) 30 and 45; LCM = 9
L) 48 and 60; LCM = 24
Once you learn this trick, have fun using it, as it is a real time-saver!
Josh Rappaport is the author of the Algebra Survival Guide: a Conversational Handbook for the Thoroughly Befuddled, available through Amazon and bookstores nationwide. Josh blogs at Http://www.mathchat.wordpress.com and tutors nationwide through his website:
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