Waste less time on Facebook — follow Brilliant.
×

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!

Note by Tan Li Xuan
4 years, 5 months ago

No vote yet
2 votes

Comments

Sort by:

Top Newest

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

Log in to reply

@Kiran Patel Can you explain why? Tan Li Xuan · 4 years, 5 months ago

Log in to reply

@Tan Li Xuan 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 · 4 years, 5 months ago

Log in to reply

@Kiran Patel Thanks! Tan Li Xuan · 4 years, 5 months ago

Log in to reply

@Tan Li Xuan yeah Superman Son · 4 years, 5 months ago

Log in to reply

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

Log in to reply

@Bhargav Das \((a,b)\) is the greatest common divisor of integers \(a,b\). Similarly, \([a,b]\) is the least common multiple of \(a,b\). O B · 4 years, 5 months ago

Log in to reply

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

Log in to reply

@Bhargav Das 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 · 4 years, 5 months ago

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

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...