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!

Note by Tan Li Xuan
5 years, 7 months ago

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

- 5 years, 7 months ago

Can you explain why?

- 5 years, 7 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...........

- 5 years, 7 months ago

Thanks!

- 5 years, 7 months ago

yeah

- 5 years, 7 months ago

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

- 5 years, 7 months ago

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

- 5 years, 7 months ago

what is the book?

- 5 years, 7 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.

- 5 years, 7 months ago

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

- 5 years, 7 months ago