L.C.M. of $12, 24$ and $36$ is equal to ?

36

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24

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72

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108

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Solution

The correct option is D $72$
First we write all numbers as product of their prime numbers.
So,
$12 = 2 \times 2 \times 3$
$24 = 2 \times 2 \times 2 \times 3$
$36 = 2 \times 2 \times 3 \times 3$

We then choose each prime number with the greatest power and multiply them to get the LCM.
$∴ L C M = 2 \times 2 \times 2 \times 3 \times 3 = 8 \times 9 = 72$

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H.C.F. of 3240, 3600 and a third number is 36 and their L.C.M. is 2 $^{4}$ x 3 $^{5}$ x 5 $^{2}$ x 7 $^{2}$ . The third number is ____.

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36

\frac{12}{24}

\frac{36}{72}

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