What is the difference between the lcm and the gcd of 24 32 and 40
The least common multiple (LCM) and greatest common divisor (GCD) are two different mathematical concepts used in number theory.
The least common multiple (LCM) of three numbers is the smallest number that is a multiple of all three numbers.
To find the LCM of 24, 32, and 40, we can list out the multiples of these numbers and find the smallest common multiple:
Multiples of 24: 24, 48, 72, 96, 120, ...
Multiples of 32: 32, 64, 96, 128, 160, ...
Multiples of 40: 40, 80, 120, 160, 200, ...
We can see that the smallest common multiple is 120. Therefore, the LCM of 24, 32, and 40 is 120.
On the other hand, the greatest common divisor (GCD) of three numbers is the largest positive integer that divides each of the three numbers without leaving a remainder.
To find the GCD of 24, 32, and 40, we can find the common factors of these numbers:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
The largest common factor is 8. Therefore, the GCD of 24, 32, and 40 is 8.
In summary,
LCM of 24, 32, and 40: 120
GCD of 24, 32, and 40: 8