Question 36731: I am trying to help my child complete an extra credit paper from edHelper.com but I cannot find any info on how to work this out. It's like you need to work backward instead of forward to get it, but after several hours, we just can't figure it out! Thanks for any help you can offer.
"Identify two numbers whose GCF is 12 and whose LCM is 396. Describe how you found the number."
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! I am trying to help my child complete an extra credit paper from edHelper.com but I cannot find any info on how to work this out. It's like you need to work backward instead of forward to get it, but after several hours, we just can't figure it out! Thanks for any help you can offer.
"Identify two numbers whose GCF is 12 and whose LCM is 396. Describe how you found the number."
WELL THE EASIEST ANSWER IS THAT GCF AND LCM THEMSELVES COULD BE THE 2 NUMBERS!!!
ANY WAY I AM GIVING BELOW AN ANALYSIS TO FIND OTHER ANSWERS AND THE APPROACH THEORY.
THERE IS A FORMULA THAT
PRODUCT OF 2 NUMBERS = PRODUCT OF THEIR LCM AND GCF
SO IF THE 2 NUMBERS ARE X AND Y SAY THEN
X*Y=12*396.................I
NOW 12 IS GCF MEANS 12 DIVIDES BOTH NUMBERS..THAT IS
X=12A WHERE A IS AN INTEGER AND
Y=12B WHERE B IS AN INTEGER AND MOST IMPORTANTLY A AND B HAVE NO FURTHER COMMON DIVISORS SINCE 12 IS GCF.
SO WE HAVE
12A*12B=12*396
A*B=396/12=33
SO WE HAVE TO FIND BY GUESS 2 FACTORS A AND B FOR 33 WHICH ARE PRIME TO EACH OTHER THAT IS WHICH DO NOT HAVE COMMON FACTORS..NOW
33=1*33.....SO A=1 AND B=33...THEN THE 2 NUMBERS COULD BE 12A=12 AND 12B=396...THAT IS THE GCF AND LCM THEMSELVES COULD BE THE 2 NUMBERS..OR
33=3*11...SO A=12*3=36 AND 12B=12*11=132 COULD BE THE 2 NUMBERS
SO WE GOT 2 SETS OF ANSWERS
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