2 natural numbers x and y such that LCM of x,y is 2 power a into 3 power b into 7 power c HCF of x,y 2 power m into 7 power n
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A
1 or 2
Suppose the HCF of (x−y,x+y) is m.
∴
x−y
m
and
x+y
m
∴ x−y=am and x+y=bm
∴ 2x=(a+b)m
Also 2y=(b−a)m
Now HCF of (x,y)=1
∴ 2 HCF of (x,y)=2
HCF of ((a+b)m,(b−a)m) is 2
m× HCF of (a+b,b−a)=2×1=2
∴ m=1 or 2.
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