20, 25 and 50
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.
3, 5 and 15
3 and 4
3 and 360
13 and 3
3 and 17
When the numbers are co-prime, ie have no common factor. Simplest example is 2 & 3 whose LCM is 6
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).
12 and 15 have a sum of 27 and a difference of 3. Their LCM is 60.
60
75 is LCM The numbers are 15 and 25 15 + 25 = 40 25 - 15 = 10 75 / 15 = 5 75 / 25 = 3
The GCF and LCM of 10 and 10 is 10.
Expressing both numbers as the product of prime numbers helps in finding out what is shared by both numbers. 100 = 2 x 2 x 5 x 5 117 = 3 x 3 x 13 It can be seen that nothing is common between 100 and 17 or in simple words the GCF is 1. For two numbers p and q where GCF(p, q) is r then LCM = (p*q)/r So, LCM is equal to product to 100 and 170 divided by 1. LCM(100, 117) = 11700.