Can two no. Have HCF as 15 And LCM as 175, Give Reasons
Answers
Answered by
283
For 2 or more numbers,
LCM=Product of highest power of each factor involved in the numbers.
HCF=Product of smallest power of each common factor.
∴We can conclude that LCM is always a multiple of HCF, i.e.,
LCM = k × HCF
We are given that
LCM = 175
HCF = 15
But in this case, LCM ≠ k × HCF.
Therefore, 2 numbers can't have LCM as 175 and HCF as 15.
LCM=Product of highest power of each factor involved in the numbers.
HCF=Product of smallest power of each common factor.
∴We can conclude that LCM is always a multiple of HCF, i.e.,
LCM = k × HCF
We are given that
LCM = 175
HCF = 15
But in this case, LCM ≠ k × HCF.
Therefore, 2 numbers can't have LCM as 175 and HCF as 15.
Answered by
167
NO! Two numbers cannot have
HCF as 15 and LCM as 175 .
Because
LCM>HCF and HCF of the two numbers should divide the LCM completely.
Here
, the 1st criteria is fulfilled but the 2nd criteria is not.
Since
175/15=35/3= 11 2/3 ∉
N.
175
is not completely divisible by 15.
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