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Algebra AMC-8 Math Olympiad Number Theory

Least common multiple | AMC 8, 2016 – Problem 20

Try this beautiful problem from Algebra based on Division algorithm (Least Common Multiple) You may use sequential hints to solve the problem.

LCM – AMC 8, 2016 – Problem 20


The least common multiple of a and b is 12 .and the lest common multiple of b and c is 15.what is the least possible value of the least common multiple of a and c?

  • 30
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  • 20

Key Concepts


Algebra

Division algorithm

Integer

Check the Answer


Answer:20

AMC-8, 2016 problem 20

Challenges and Thrills of Pre College Mathematics

Try with Hints


Find greatest common factors

Can you now finish the problem ……….

Find Least common multiple….

can you finish the problem……..

we wish to find possible values of a,b and c .By finding the greatest common factor 12 and 15, algebrically ,it’s some multiple of b and from looking at the numbers ,we are sure that it is 3.Moving on to a and c ,in order to minimize them,we wish to find the least such that the LCM of a and 3 is 12,$\to 4$.similarly with 3 and c,we obtain 5.the LCM of 4 and 5 is 20 .

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