The sum of two numbers is 35, and their LCM is 306. The two numbers are:

Question

Examoogle · Accepted Answer

The correct answer is Option A: 17, 18. Since the sum is 35, test pairs of numbers summing to 35: (18, 17), (19, 16), (22, 13), (21, 14). Check if their LCM is 306. $18 	imes 17 = 306$, and since 17 is prime, the LCM of 18 and 17 is indeed 306.

Step-by-Step Solution & Concepts:
Shortcut Trick: Since the sum is 35, test pairs of numbers summing to 35: (18, 17), (19, 16), (22, 13), (21, 14). Check if their LCM is 306. $18 	imes 17 = 306$, and since 17 is prime, the LCM of 18 and 17 is indeed 306.

Formula Used: $$x + y = 35$$, $$LCM(x, y) = 306$$

Given: Sum of two numbers is 35, and their LCM is 306.

Steps: Formulate equations: Let the two numbers be $x$ and $y$. We are given their sum is 35 and their LCM is 306.. Analyze the sum and LCM: Test the provided options to see which pair satisfies the sum condition and yields the LCM of 306. Check pair (18, 17): $18 + 17 = 35$. The prime factorization of 18 is $2 	imes 3^2$ and 17 is $17^1$.. Verify result: Since 17 is a prime number and not a factor of 18, their greatest common divisor is 1. Thus, their LCM is their product.

Answer: A is correct because the numbers 18 and 17 add up to 35 and their least common multiple is $18 	imes 17 = 306$.

Exam Tip: In competitive exams, when the sum and product (or LCM) are given, always check the factors of the LCM first, as it limits the search space significantly.

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