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Number Theory

Greatest Common Divisor / Lowest Common Multiple

GCD and LCM - Problem solving


If the lowest common multiple of \(4,6,8,9,\) and \(x\) is \(504,\) what is the third smallest possible integer \(x?\)

Note: Third smallest means the third value of \(x\) if the possible values were listed from least to greatest.

What is the largest 3-digit number that is a multiple of 12 and a multiple of 21, but not a multiple of 22?

If the greatest common divisor of \(266,308,392,\) and \(x\) is \(7,\) what is the sum of the smallest and largest possible 2-digit positive integers \(x?\)

\(A\) and \(B\) are positive integers such that \[\begin{array} &\gcd(A,B)= 9, &\mbox{lcm}(A,B) = 180, &A<B. \end{array}\] How many such \(A\)'s are there?

What is the lowest common multiple of the numbers 8, 9, 10, and 12?


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