which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, 10 is 4? Choose the correct choice
A) 168
B) 172
C) 182
D) 140
E) 160
<gadget id="calculator">lcm(7, 12)</gadget>
<output>84</output>

<gadget id="calculator">lcm(84, 10)</gadget>
<output>420</output>

<gadget id="calculator">gcd(1_856, 420)</gadget>
<output>4</output>

<gadget id="calculator">4 * 420</gadget>
<output>1_680</output>

<gadget id="calculator">4 + 1_680</gadget>
<output>1_684</output>

<gadget id="calculator">1_856 - 1_684</gadget>
<output>172</output>

<result>B</result>
which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, 10 is 4?
subtract(1856, add(4, multiply(gcd(1856, lcm(lcm(7, 12), 10)), lcm(lcm(7, 12), 10))))
first we need to figure out what numbers are exactly divisible by 7 , 12,10 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,10 ) = 42 * 10 = 420 the numbers which will leave remainder 4 will be { 420 + 4 , 420 x 2 + 4 , , . . . } the largest such number less than or equal to 1856 is 420 * 4 + 4 or 1684 to obtain this you need to subtract 172 . b