Hi everybody,I have a question on olympiad maths (Not from brilliant's problems) that I'm unable to solve.The question is:If \( a+b=432 \) and \( (a,b)+[a,b]=7776 \),find \( ab \).Please help me.Thanks!

Gcd of a and b must divide 432,so their Gcd must be a divisor of 432.We see that higher divisors of 432 like 216,108 cant be the Gcd and lower one like 2,3 also can't be the Gcd,so checking the middle ones we get Gcd = 6 so,further simplification gives us the answer...........

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TopNewesta=210, b=222, ab=46620.

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Can you explain why?

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Gcd of a and b must divide 432,so their Gcd must be a divisor of 432.We see that higher divisors of 432 like 216,108 cant be the Gcd and lower one like 2,3 also can't be the Gcd,so checking the middle ones we get Gcd = 6 so,further simplification gives us the answer...........

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yeah

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can u explain me the meaning of - (a,b)+[a,b]=7776

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\((a,b)\) is the greatest common divisor of integers \(a,b\). Similarly, \([a,b]\) is the least common multiple of \(a,b\).

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what is the book?

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It's not a book.It's from the 2012 IMAS upper primary question paper.I was practicing for this year's IMAS.

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Hint: Use the fact that \((a,b)[a,b]=ab\) for positive integers \(a,b\).

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