20, 25 and 50
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Oh, dude, like, I got you! So, the LCM of 100 is, well, 100. You can have 1, 100, and 1, or 2, 50, and 1, or even 4, 25, and 1. Basically, any combo where the numbers multiply to 100 works! Math can be chill like that, you know?
Well, isn't that just a happy little math question! To find three numbers whose least common multiple (LCM) is 100, we can choose numbers that have common factors with 100. One example could be 20, 25, and 100, as their LCM would be 100. Just remember, there are many combinations that could work, so feel free to explore and see what you come up with!
Well, honey, the LCM of a set of numbers is the smallest number that all those numbers can divide into evenly. So, for 100, you could have 1, 100, and 100. Or, you could have 2, 50, and 100. Or, you could have 4, 25, and 100. It's a multiple choice of options, darling.
The set of three numbers whose LCM (Least Common Multiple) is equal to the product of the numbers would be {1, 2, 2}. Here's how it works: LCM(1, 2, 2) = 2, which is also the product of the numbers (1 * 2 * 2 = 4).
63 = 3 x 3 x 7, so there are more than one combination: 7 & 9 and 21 & 9. That should be it, unless you want to consider the somewhat trivial combinations : 63 & 21, 63 & 9, 63 & 3, 63 & 7.
The LCM of 3 and 9 is 9.
84, 96 and 108
The two numbers 18 and 27. Factorising the lcm and gcf gives: 54 = 2 × 3³ 9 = 3² There must be 3² in both numbers, but there must be a 3³ and a 2 which must appear in the prime factorisations of the two numbers. Putting a 2 with one 3² and a 3 with the other 3² leads to the two numbers: 2 × 3² = 18 3 × 3³ = 3³ = 27 as the two smallest numbers with gcf=9 and lcm=54. The other distribution of both 2 and 3 with one 3² results in the two number 3² = 9 and 2 × 3³ = 54, the latter of which is larger than both the 18 and 27 previously found.