Question numbers 7 to 12 carry 2 marks each.7. Can two numbers have 15

1.	Question numbers 7 to 12 carry 2 marks each.7. Can two numbers have 15 as their HCF and 175 as their LCM ? Give reasons.
Answer» For two 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, two numbers can't have LCM as 175 and HCF as 15.

Question numbers 7 to 12 carry 2 marks each.7. Can two numbers have 15 as their HCF and 175 as their LCM ? Give reasons.

Answer»

For two 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, two numbers can't have LCM as 175 and HCF as 15.