# Ex.1.2 Q3 Real Numbers Solution - NCERT Maths Class 10

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## Question

Find the LCM and HCF of the following integers by applying the prime factorisation method.

(i)  $$12, 15$$ and $$21$$

(ii)  $$17, 23$$ and $$29$$

(iii)  $$8, 9$$ and $$25$$

Video Solution
Real Numbers
Ex 1.2 | Question 3

## Text Solution

What is known?

(i)  $$12, 15$$ and $$21$$

(ii)  $$17, 23$$ and $$29$$

(iii)  $$8, 9$$ and $$25$$

What is unknown?

The LCM and HCF of the given integers by applying the prime factorisation method.

Reasoning:

To solve this question, follow the following steps-

• First find the prime factors of the given integers.
• Find the HCF of the given pair of integers i.e. product of smallest power of each prime factor, involved in the number.
• Lastly, Find the LCM of the given pair of integers i.e. product of greatest power of each prime factor, involved in the number.

Steps:

(i) $$12, 15$$ and $$21$$

Prime factors of $$12$$

\begin{align}&= {2 \times 2 \times 3}\\&={{2^2} \times 3}\end{align}

Prime factors of $$15= 3 \times 5$$

Prime factors of $$21=2 \times 2 \times 3$$

HCF of $$12,15$$ and $$21= {3}$$

LCM of $$12,15$$ and $$21$$  \begin{align}&= {{2^2} \times 3 \times 5 \times 7}\\ &={ 420}\end{align}

(ii) $$17, 23$$ and $$29$$

Prime factors of $$17= 17\,\times\,1$$

Prime factors of $$23=23\,\times\,1$$

Prime factors of $$29 = 29 \times 1$$

HCF of $$7,\,23$$ and $$29={1}$$

LCM of $$17,\,23$$ and $$29$$

\begin{align}&= 17 \times 23 \times 29\\&= 11339\end{align}

(iii) $$8, 9$$ and $$25$$

Prime factors of $$8$$

\begin{align}&= 2 \times 2 \times 2\\ &= {2^3}\end{align}

Prime factors of $$9$$

\begin{align}&= 3 \times 3\\ &= {3^2}\end{align}

Prime factors of $$25$$

\begin{align}&= 5 \times 5\\ &= {\text{ }}{5^2}\end{align}

HCF of $$8, 9$$ and $$25 = 1$$

LCM of $$8,\,9$$ and $$25$$

\begin{align} &=2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5 \\ &=1800 \end{align}

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