Question

find hcf and lcm of (m^2-2m-15), (m^3-125-15m^2+75m)and (m^2-125).​

Answer 1

Answer:

The HCF is ( m - 5 )

The LCM is ( m - 5 )³ ( m + 3 ) ( m² + 5m + 25 )

Step-by-step explanation:

I'm going to guess that you actually meant to write m³-125 for the third one as that makes the question more like a typical exercise.  Hope that's correct!

Factorize:

• m² - 2m - 15 = ( m - 5 ) ( m + 3 )
• m³ - 125 = m³ - 5³ = ( m - 5 ) ( m² + 5m + 25 )
• m³ - 15m² + 75m - 125 = m³ - (3)(5)m² + (3)(5²)m - 5³ = ( m - 5 )³

So the HCF is ( m - 5 ), as this divides all three and nothing more is common to all three.

The LCM is ( m - 5 )³ ( m + 3 ) ( m² + 5m + 25 ), as this is divisible by all three above and nothing less will do.