Question

A heap of stones can be made up into groups of 21 When made up into groups of 16, 20, 25 and 45 there are 3 stones left in each case. How many stones at least can there be in the heap?

• A. $7203$
• B. $2403$
• C. $3603$
• D. $4803$

Answer 1

The correct option is A $7203$

LCM of (16, 20, 25, 45) $=3600$
So number of stones=$3600k+3$
Since the stones can be made up into groups of 21
$\therefore$ 9k + 3 is divisible by 21 when k = 2
$\therefore Leastnumberofstones=3600\times 2+3=7203$