[求助]PP-DS-1-142

chiachen1223

請各位幫忙解惑!謝謝!

142. If x is a positive integer, what is the least common multiple of x, 6, and 9 ?

(1)  The least common multiple of x and 6 is 30.

 (2)  The least common multiple of x and 9 is 45.

ANS

iloverainbow

如果（1）或者（2）单独成立。都能求出x=5

迷途小孩

有点疑问 题目没有说x is prime number
1.x可以取值 5，10，15，30
2.x可以取值5，15，45
自己推算了一下 虽然结果貌似是相同的 但是道理想不明白
求助nn们

飞天小牛牛

I agree with D Question is not about the value of x, it is about the LCM of three intergers The key here is prime factorisation rephrasing the main statement: What is LCM of x, 2*3 (6=2*3), and 3^2 (9=3*3) (1) LCM of x and 2*3 is 30. Factoring 30=2*3*5 this means that x has 5 as a factor. x can contain 2 and 3 but not necessary answering the main question: LCM of 2*3, 3^3 and x is 2*3^2*5=90 Let's check x=5. LCM of 5, 6 and 9 is 90 x=10. LCM = 90 x=15. LCM = 90 SUFF (2) Using the same logic LCM of x and 3^2 is 45 45 = 3^2*5 x has 5 as a factor LCM of 5, 6 and 9 is 90 SUFF Answer D Remember, that LCM of 2 or more numbers is a product of all prime numbers, included into prime factorization at least one of these numbers, raised to the highest of two powers GCD of 2 or more numbers is a product of prime numbers, included into prime factorization of all numbers, and raised to the smallest of two powers