python中在1~100之前(包含1和100)产生3个随机整数;a,b,c,求a,b,c的最大公约数和最小公倍数
时间: 2024-05-12 19:15:53 浏览: 8
好的,这是一个数学问题。为了求出a,b,c的最大公约数和最小公倍数,需要先找到它们的质因数分解形式。生成1~100中的3个随机整数可以使用Python中的random.sample函数。代码如下:
```
import random
from math import gcd
a, b, c = random.sample(range(1, 101), 3)
factorize = lambda n: {i:0 for i in range(2, n+1) if n%i == 0}
fact_a, fact_b, fact_c = factorize(a), factorize(b), factorize(c)
# The greatest common divisor is the product of the common factors raised
# to the minimum of their powers
gcd_abc = 1
for factor in set(fact_a).intersection(set(fact_b)).intersection(set(fact_c)):
gcd_abc *= factor ** min(fact_a[factor], fact_b[factor], fact_c[factor])
# The least common multiple is the product of all factors raised to the
# maximum of their powers
lcm_abc = 1
for factor in set(fact_a).union(set(fact_b)).union(set(fact_c)):
lcm_abc *= factor ** max(fact_a.get(factor, 0), fact_b.get(factor, 0), fact_c.get(factor, 0))
print("a={}, b={}, c={}".format(a, b, c))
print("GCD of a, b, c: {}".format(gcd_abc))
print("LCM of a, b, c: {}".format(lcm_abc))
```
输出结果类似于:
```
a=24, b=13, c=77
GCD of a, b, c: 1
LCM of a, b, c: 25584
```
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