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CTET Paper II (Mathematics and Science) Sep 2015 Solved Paper

Question : 32 of 150

Marks: +1, -0

LCM of 22, 54, 135 and 198 is

$2^{2}\times 3^{3}\times 5\times 11$
$2\times 3^{3}\times 5\times 11$
$2\times 3^{3}\times 5^{2}\times 11$
$2^{3}\times 3^{2}\times 5\times 11$

Solution:

Concept:

LCM is the smallest common multiple. Use prime factorization: write each number as product of primes, then LCM takes each prime with its highest power from any number.

Explanation:

First, factorize each number:

22 = 2 \times 11

54 = 2 \times 3^{3}

135 = 3^{3} \times 5

198 = 2 \times 3^{2} \times 11

Now, take the highest power of each prime appearing in any factorization:

Prime 2: highest power is

2^{1}

(from 22, 54, or 198).

Prime 3: highest power is

3^{3}

(from 54 or 135).

Prime 5: highest power is

5^{1}

(from 135).

Prime 11: highest power is

11^{1}

(from 22 or 198).

Multiply them:

2 \times 3^{3} \times 5 \times 11

Answer:

Option B:

2\times 3^{3}\times 5\times 11

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