Find the LCM of 216 and 240.

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2160

216

192

answer is A.

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Detailed Solution

Concept- First, write the product of prime factors of each number and then choose the common and uncommon prime factors with the greatest exponent. To find the LCM, multiply the common and uncommon prime factors with the greatest exponents.
LCM of 216 and 240
Using the prime factorization method, write the prime factors as product of numbers
First for, 216

216 = 2 \times 2 \times 2 \times 3 \times 3 \times 3

Similarly for, 240
240=2×2×2×2×3×5
Further simplifying, 216 and 240 as

216 = 2^{3} \times 3^{3}

and

240 = 2^{4} \times 3 \times 5

Common prime factors are

2, 3

Common prime factors with the greatest exponent are

2^{4}, 3^{3}

Uncommon prime factor is 5
Uncommon prime factor with the greatest exponent are

5^{1}

So, LCM of 216 and 240 can be obtained by

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

Now simplifying,

2^{4} \times 3^{3} \times 5 = 2160

2160 is the least number which is completely divisible by both numbers 216 and 240.
Therefore, the LCM of 216 and 240 is 2160.
Hence, the correct option is 1.

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