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Greatest Common Divisor / Lowest Common Multiple
What is the largest number that can divide two numbers without a remainder? What is the smallest number that is divisible by two numbers without a remainder?
\[\huge \color{red}{2}, \color{green}{-4}\]
Find the lowest common multiple of the two numbers above.
by
Sandeep Bhardwaj
\[\LARGE \color{blue}{0.\bar{3}}, \color{red}{0.\bar{5}}\]
What is the lowest common multiple of the two numbers given above?
Note that \(0. \overline{ABC} = 0.ABCABCABC\ldots \).
by
Sandeep Bhardwaj
How many positive integers \(a\) are there such that 2027 divided by \(a\) leaves a remainder of 7?
by
Calvin Lin
Evaluate \( \gcd ( 19 ! + 19, 20! + 19 ) \).
Details and assumptions
The number \( n!\), read as n factorial, is equal to the product of all positive integers less than or equal to \(n\). For example, \( 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\).
by
Calvin Lin
How many ordered pairs of positive integers \( (m, n)\) satisfy
\[ \gcd (m^3, n^2) = 2^2 \cdot 3^2 \text{ and } \text{lcm}(m^2, n^3) = 2^4 \cdot 3^4 \cdot 5^6? \]
This problem is shared by Muhammad A.
Details and assumptions
\( \gcd(a, b) \) and \( \text{lcm}(a, b) \) denote the greatest common divisor and least common multiple of \( a \) and \( b \), respectively.
by
Calvin Lin