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!

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TopNewesta=210, b=222, ab=46620. – Kiran Patel · 4 years, 5 months ago

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– Tan Li Xuan · 4 years, 5 months ago

Can you explain why?Log in to reply

– Kiran Patel · 4 years, 5 months ago

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...........Log in to reply

– Tan Li Xuan · 4 years, 5 months ago

Thanks!Log in to reply

– Superman Son · 4 years, 5 months ago

yeahLog in to reply

can u explain me the meaning of - (a,b)+[a,b]=7776 – Bhargav Das · 4 years, 5 months ago

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– O B · 4 years, 5 months ago

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

what is the book? – Bhargav Das · 4 years, 5 months ago

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– Tan Li Xuan · 4 years, 5 months ago

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

Hint: Use the fact that \((a,b)[a,b]=ab\) for positive integers \(a,b\). – David Altizio · 4 years, 5 months ago

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