Question

Can two numbers have 15 as their hcf and 175 as their lcm. Give reasons?

Answer 1

Of course they can have these numbers as their hcf

Answer 2

Answer:

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.