What is the L.C.M. of 180, 384, and 144?

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5750

5770

5765

5760

answer is D.

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Detailed Solution

Given data,
180, 384, and 144.
Let’s calculate the prime factors of the given numbers.
The prime factorization of 180, 384, and 144,

180 = 3 \times 3 \times 2 \times 2 \times 5

384 = 3 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2

144 = 3 \times 3 \times 2 \times 2 \times 2 \times 2

Calculating the LCM of 180, 384 and 144,
LCM

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5

LCM = 5760
Therefore, the LCM of 180, 384, 144 is 5760.
Hence, option 4 is correct.

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