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ProfessorWell, 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!
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What set of 3 numbers whose LCM is the product of the number?
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).
What are the two numbers whose LCM is 63?
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.
What numbers have a square LCM?
The LCM of 3 and 9 is 9.
What 3 numbers whose gcf is 12 with one of the numbers being greater than 100?
84, 96 and 108
What are the two smallest numbers whose gcf is 9 and whose LCM is 54?
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.
