Find the LCM of 2^{4} × 3^{5} × 6³ × 7², 2^{5} × 3² × 6¹ × 7^{5} and 2³ × 3^{4} × 6² × 7¹ × 9²

Correct Answer is : None of these

2^{4} × 3² × 6² × 7¹ × 9²

2³ × 3² × 6¹ × 7¹ × 9²

2^{5} × 3^{5} × 6³ × 7^{5} × 9²

Correct Answer is : None of these

Test Index

LCM and HCF Practice Test 3

Question : 10 of 40

Marks: +1, -0

Find the LCM of

2^{4} \times 3^{5} \times 6^{3} \times 7^{2}

2^{5} \times 3^{2} \times 6^{1} \times 7^{5}

2^{3} \times 3^{4} \times 6^{2} \times 7^{1} \times 9^{2}

Solution:

Concept:

LCM of factorized numbers is found by taking the highest power of every prime factor.

Explanation:

Convert composite bases into prime factors:

6=2\times3

and

9=3^2

First number:

2^4\cdot3^5\cdot6^3\cdot7^2=2^4\cdot3^5\cdot(2\cdot3)^3\cdot7^2=2^7\cdot3^8\cdot7^2

Second number:

2^5\cdot3^2\cdot6^1\cdot7^5=2^5\cdot3^2\cdot(2\cdot3)\cdot7^5=2^6\cdot3^3\cdot7^5

Third number:

2^3\cdot3^4\cdot6^2\cdot7^1\cdot9^2=2^3\cdot3^4\cdot(2\cdot3)^2\cdot7\cdot(3^2)^2=2^5\cdot3^{10}\cdot7

Take maximum powers:

2^{\max(7,6,5)}=2^7

3^{\max(8,3,10)}=3^{10}

7^{\max(2,5,1)}=7^5

So, LCM

=2^7\cdot3^{10}\cdot7^5

This is not present in options A to D.

Answer:

E. None of these

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