25. Write HCF and LCM of the smallest odd composite number and the smallest odd prime number. If an odd number p divides 9then will it divide q’ also? Explain.
2 thoughts on “25. Write HCF and LCM of the smallest odd<br />composite number and the smallest odd<br />prime number. If an odd number p divides”
Answer:
q² × q = q³, and p is a factor of q², hence it will also be a factor of q² × q. Therefore, p will divide q³ also. In general, we can say that if p divides q² then it will also divide qⁿ, where n is a natural number (n ≥ 2).
We also know that LCM is the smallest possible number that is a multiple of them. So, from the factorisation of 3 and 9, we can say that 9 is the LCM of 3 and 9. Hence, we can say that the HCF and LCM of the smallest odd composite number and the smallest odd prime number are 3 and 9 respectively.
Answer:
q² × q = q³, and p is a factor of q², hence it will also be a factor of q² × q. Therefore, p will divide q³ also. In general, we can say that if p divides q² then it will also divide qⁿ, where n is a natural number (n ≥ 2).
Answer:
We also know that LCM is the smallest possible number that is a multiple of them. So, from the factorisation of 3 and 9, we can say that 9 is the LCM of 3 and 9. Hence, we can say that the HCF and LCM of the smallest odd composite number and the smallest odd prime number are 3 and 9 respectively.