Telangana Board Solutions for Chapter: Real Numbers, Exercise 8: Exercise

Find the $\mathrm{LCM}$ and $\mathrm{HCF}$ of $12$, $15$ and $21$ by the prime factorization method.

Find the $\mathrm{LCM}$ and $\mathrm{HCF}$ of $17$, $23$ and $29$ by the prime factorization method.

Find the $\mathrm{LCM}$ and $\mathrm{HCF}$ of $8$, $9$ and $25$ by the prime factorization method.

Find the $\mathrm{LCM}$ and $\mathrm{HCF}$ of $72$ and $108$ by the prime factorization method.

Find the $\mathrm{LCM}$ and $\mathrm{HCF}$ of $306$ and $657$ by the prime factorization method.

Explain why $7\times 11\times 13+13$ and $7\times 6\times 5\times 4\times 3\times 2\times 1+5$ are composite numbers.

How will you show that $(17\times 11\times 2)+(17\times 11\times 5)$ is a composite number? Explain.

What is the last digit of $6^{100}$?