Mathematics

First factor each of the three Natural numbers into their primes. Then multiply the highest power of each prime together. This will be the LCM.

Let me give you some examples:

The LCM of 12, 72, 54

12=2^2 * 3

72=2^3 * 3^2

54=2 * 3^3

Therefore the LCM is 2^3 * 3^3 = 8*27 = 216

Notice that the highest power for 2 was 3, and the highest power of 3 was 3. No other primes are involved.

Now the LCM of {2,3,5) is just the product of all three, because all three are primes, and thus the LCM is 2*3*5=30. The LCM is the smallest Natural number that is a multiple of each of the three numbers.

Thomas Fuller, an African sold into slavery in 1724 at the age of 14, was sometimes known as the “Virginia Calculator” for his extraordinary ability to solve complex math problems in his head. He was asked how many seconds there were in a year and a half, he answered in about two minutes, 47,304,000. Again he was asked how many seconds a man has lived who is 70 years, 17 days and 12 hours old, he answered in a minute and a half 2,210,500,800.

One of the men was working out the problems on paper, and informed Fuller that he was wrong, because the answer was much smaller. Fuller hastily replied, "'Top, massa, you forget de leap year." When the leap year was added in, the sums matched.

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