Question

The least number which when divided by 36, 48, and 64 leaves remainders 25, 37, and 53, respectively, is

• A. 515
• B. 535
• C. 565
• D. 585

Answer 1

The correct option is C 565

Since $36-25=48-37=64-53=11$
Least number = $(LCMof36,48and64)-11$

$2$	$36$	$48$	$64$
$2$	$18$	$24$	$32$
$3$	$9$	$12$	$16$
$2$	$3$	$4$	$16$
$2$	$3$	$2$	$8$
	$3$	$1$	$4$

$LCM=2\times 2\times 3\times 2\times 2\times 3\times 4=576$
$=576-11$
$=565$