can two numbers have a HCF of 14 and LCM of 204? give reasons for your answer
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Step-by-step explanation:
No,
Let X and Y be our two numbers,
And
X=14a
Y =14b
Where a,b are Co prime to each other
To find the LCM,
LCM = 14ab
According to question
LCM = 204
204 = 14ab
14.5714.... = ab
Because a and b are Co prime integers
a*b cannot be a fraction.
Therefore, 204 cannot be the LCM if 14 is the HCF.
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