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Question Number 104280 by Anindita last updated on 20/Jul/20

What is the GCD of (1/2), (3/4), ((16)/(30)) ?

$$\boldsymbol{\mathrm{What}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{GCD}}\:\boldsymbol{\mathrm{of}}\: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{3}}{\mathrm{4}},\:\frac{\mathrm{16}}{\mathrm{30}}\:? \\ $$

Commented by 1549442205PVT last updated on 20/Jul/20

Can you tell me what is brief word”GCM”?

$$\mathrm{Can}\:\mathrm{you}\:\mathrm{tell}\:\mathrm{me}\:\mathrm{what}\:\mathrm{is}\:\mathrm{brief} \\ $$$$\mathrm{word}''\mathrm{GCM}''? \\ $$

Commented by bramlex last updated on 20/Jul/20

greatest common multiple?

$${greatest}\:{common}\:{multiple}? \\ $$

Commented by Anindita last updated on 20/Jul/20

Yes

$$\mathrm{Yes} \\ $$

Commented by Rasheed.Sindhi last updated on 20/Jul/20

Perhaps you mean LCM (least common multiple) or GCD(greatest common divisor).

$${Perhaps}\:{you}\:{mean}\:\mathrm{LCM}\: \\ $$$$\left({least}\:{common}\:{multiple}\right)\:{or} \\ $$$$\mathrm{GCD}\left({greatest}\:{common}\right. \\ $$$$\left.{divisor}\right). \\ $$

Commented by 1549442205PVT last updated on 21/Jul/20

But LCM and GCD only say in integers?Here all are fractions?

$$\mathrm{But}\:\mathrm{LCM}\:\mathrm{and}\:\mathrm{GCD}\:\mathrm{only}\:\mathrm{say}\:\mathrm{in} \\ $$$$\mathrm{integers}?\mathrm{Here}\:\mathrm{all}\:\mathrm{are}\:\mathrm{fractions}? \\ $$

Answered by Rasheed.Sindhi last updated on 24/Jul/20

LCM of denominators=60 (1/2)=((30)/(60)) , (3/4)=((45)/(60)) ,((16)/(30))=((32)/(60)) Now GCD of numerators 30,45,32 =1 So GCD of the given fractions is (1/(60)) (We have 30 sixtieths,45 sixtieths & 32 sixtieths.You can see that 1 sixtieth(1/60) is a common divisor and it′s also greatest common divisor,b/c there is no common divisor greater than this.)

$${LCM}\:{of}\:{denominators}=\mathrm{60} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}=\frac{\mathrm{30}}{\mathrm{60}}\:,\:\frac{\mathrm{3}}{\mathrm{4}}=\frac{\mathrm{45}}{\mathrm{60}}\:,\frac{\mathrm{16}}{\mathrm{30}}=\frac{\mathrm{32}}{\mathrm{60}} \\ $$$${Now}\:{GCD}\:{of}\:{numerators} \\ $$$$\mathrm{30},\mathrm{45},\mathrm{32}\:=\mathrm{1} \\ $$$${So}\:\mathrm{GCD}\:{of}\:{the}\:{given}\:{fractions} \\ $$$$\:{is}\:\:\frac{\mathrm{1}}{\mathrm{60}}\: \\ $$$$\left({We}\:{have}\:\mathrm{30}\:{sixtieths},\mathrm{45}\:{sixtieths}\right. \\ $$$$\&\:\mathrm{32}\:{sixtieths}.{You}\:{can}\:{see}\:{that} \\ $$$$\mathrm{1}\:{sixtieth}\left(\mathrm{1}/\mathrm{60}\right)\:{is}\:{a}\:{common}\: \\ $$$${divisor}\:{and}\:{it}'{s}\:{also}\:{greatest} \\ $$$${common}\:{divisor},{b}/{c}\:{there}\:{is}\:{no} \\ $$$$\left.{common}\:{divisor}\:{greater}\:{than}\:{this}.\right) \\ $$

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