Question 39077: Can someone out there help me with this problem?
How do you find the least common multiple (LCM) for the following group of numbers.
12, 20, and 35. Explain if you can how you come up with your answer.
Thanks!
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! LCM OF 10,20 AND 35
LEAST COMMON MULTIPLE ..THAT IS THE SMALLEST NUMBER WHICH IS DIVISIBLE BY ALL THE 3 ABOVE NUMBERS .ONE METHOD IS TO BREAK THESE NUMBERS IN TO THEIR PRIME FACTORS.THAT IS
TAKE 10...ITS FACTORS ARE 2*5
10=2*5.....................................I..SIMILARLY
20=2*2*5...............................II
35=5*7............................III
NOW TO GET LCM ,WE LOOK FOR COMMON FACTORS IN ATLEAST 2 OF THE ABOVE EQNS.I,II,III
WE FIND ONE 2 IS COMMON IN I&II
AND ONE 5 IS COMMON IN I,II,III
SO WE TAKE THOSE COMMON FACTORS,LIST THEM AND FIND THEIR PRODUCT..
LIST OF COMMON FACTORS....
2 AND 5.
THEIR PRODUCT =PCF(PRODUCT OF COMMON FACTORS)
2*5=10............................................IV
NOW WE STRIKE OUT THE COMMON FACTORS AND WE LIST THE REMAINING
NONE IN I(AS ONE 2 AND ONE 5 ARE LISTED IN COMMON FACTORS)
2 IN II (AS ONLY ONE 2 AND ONE 5 ARE LISTED IN COMMON FACTORS)
7 IN III(AS ONLY ONE 5 IS LISTED IN COMMON FACTORS)
SO LIST OF NON COMMON FACTORS..
2 AND 7
THEIR PRODUCT = PNCF
2*7=14............................................V
NOW LCM IS GIVEN BY PRODUCT OF COMMON ANF NON COMMON FACTORS..IV AND V.
LCM=10*14=140..
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