An olympiad maths problem

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!

#HelpMe! #MathProblem

Easy Math Editor

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Comments

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

David Altizio - 8 years, 3 months ago

what is the book?

Bhargav Das - 8 years, 3 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.

Tan Li Xuan - 8 years, 3 months ago

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

Bhargav Das - 8 years, 3 months ago

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

o b - 8 years, 3 months ago

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

kiran patel - 8 years, 3 months ago

Can you explain why?

Tan Li Xuan - 8 years, 3 months ago

yeah

superman son - 8 years, 3 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...........

kiran patel - 8 years, 3 months ago

@Kiran Patel – Thanks!

Tan Li Xuan - 8 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$