Monthly Archives: November 2022

What is the sum of LCM and GCD ?

Find the sum of the LCM and GCD of positive numbers and that satisfy the equation

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AIME problem on LCM

For how many values of is the least common multiple of the positive integers and ?

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Smallest number leaving same remainder of 1

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Crux argument in proof showing why every common divisor divides gcd and why every common multiple divides lcm

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Probability distribution, Picking red ball on the nth trial

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2021 AM 12A Problem 8

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Combining Two Discrete Independent Random Variables

The discrete random variables A and B are independent and have the following distributions.

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Proof GCD*LCM = ab in 3 steps

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2002 AMC 12A Problem 20

Suppose that a and b are digits, not both nine and not both zero, and the repeating decimal 0.ababab.. is expressed as a fraction in lowest terms. How many different denominators are possible ?

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2021 AMC 10A Problem 8

When a student multiplied the number 66 by the repeating decimal 1.abab… 1=ab, where a and b are digits, he did not notice the notation and just multiplied 66 times 1.ab. Later he found that his answer is 0.5 less … Continue reading

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