HCF of abc and cde is > 1 > a > b > c
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Step-by-step explanation:We have three numbers a , b , c .
Let HCF be the highest common factor of a, b and c.
a = HCF x r
b = HCF x s
c = HCF x t
Where HCF(r,s,t) = 1 since HCF(a,b,c) = HCF
Here HCF x r x s x t = LCM(a,b,c)
rstxHCF = LCM(a,b,c)
Now,
a x st = HCF x rst
b x rt = HCF x rst
c x rs = HCF x rst
Multiply all three equations,
abc x (rst)² = HCF³ x (rst)³
abc = HCF x rst x HCF²
abc = LCM x HCF²
Now HCF(ab,bc,ca) :
ab = HCF x r x HCF x s = HCF² x rs
bc = HCF x s x HCF x t = HCF² x st
ac = HCF x r x HCF x t = HCF² x rt
Therefore HCF(ab,bc,ca) = HCF²
Therefore ,
abc = LCM(a,b,c) x HCF(ab,bc,ca)
LCM(a,b,c) = abc/HCF(ab,bc,ca)
Thus proved that LCM (a,b,c)=abc\ HCF (ab,bc,ca).
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