Which of the following cannot be the least common multiple of distinct positive integers a and b?

I. 1
II. ab
III. a - b

Answer Choices

Correct answer marked below

I only

III only

I and II

I and III

Correct

II and III

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Explanation

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Official Explanation

Official

The least common multiple (LCM) of two distinct positive integers a and b must be greater than or equal to the larger of the two integers. Since both a and b are positive and distinct, their LCM cannot be…

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Comments

ChristopherMar 19, 2025

Thankss

BenSep 13, 2024

this helped me

WarisaDec 14, 2024

thank you very much!

ShahnoorJul 20, 2025

LCM has to be greater than equal to the largest number, if a> b and both are positive a-b will be less than a hence a-b will not be the lcm

What this question tests

What it tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Common trap

Forgetting that 1 is not prime and that every integer divides 0.

Which of the following cannot be the least common multiple of distinct positive integers a and b? I. 1 II. ab III. a - b