So I had to find four least common multiples done out below:
a) LCM(8,12) = 24
b) LCM(20, 30) = 60
c) LCM(51, 68) = 204
d) LCM(23, 18) = 414
For each of the LCMs computed above, I have to compare the value of LCM(a, b) to the values of a, b, and gcd(a,b) and find a relationship between the two.
So I've basically calculated the gcds and retrieved the following:
a) gcd(8,12) = 4
b) gcd(20,30) = 10
c) gcd(51,68) = 17
d) gcd(23, 18) = 1
The only relationship I've found is that the difference between a and b is the gcd for them in cases a through c. I was wondering, is there another pattern I should be aware of here?
2007-09-08 16:17:43 · 4 answers · asked by Fonzieo 1 in Science & Mathematics ➔ Mathematics
LCM = a*b / GCD(a,b)
or
LCM * GCD = a*b
2007-09-08 16:27:01 · answer #1 · answered by math_ninja 3 · 0⤊ 0⤋
here is one pattern that I notice:
a) gcd(8,12) = 4
Take the first number, 8, and divide by 4, =2.
Now, multiply the second number by 2, and you get the LCM of the pair.
8/4 = 2 ; 2*12 = 24
20/10 = 2; 2*30 = 60
51/17 = 3; 3*68 = 204
23/1 = 23; 23*18 = 414
There may be more, but that is one..
2007-09-08 16:28:30 · answer #2 · answered by Andrew B 2 · 0⤊ 0⤋
The LCM for 36 and 42 would be 252
2016-05-20 00:27:49 · answer #3 · answered by ? 3 · 0⤊ 0⤋
You're getting warm, but I think the below presentation is more to the point.
In a, b and c, none of the numbers are primes.
In the last one, 23 is prime
In a, b, and c, since 3 is a factor of at least one of the numbers, the LCM is 3 times one of them.
In d, since 23 is prime, the LCM is 23x18.
2007-09-08 16:30:42 · answer #4 · answered by cattbarf 7 · 0⤊ 0⤋