Question

The least number which when increased by $5$ is divisible by each one of $24,32,36$ and $54$ is

• A. $427$
• B. $859$
• C. $869$
• D. $4320$

Answer 1

Answer: (B)

$859$

L.C.M of $24,32,36,54$

$2|24,32,36,54$

_______________

$2|12,16,18,27$

_______________

$9|6,8,9,27$

_______________

$2|6,8,1,3$

_______________

$3|3,4,1,3$

_______________

$4|1,4,1,1$

_______________

$1,1,1,1$

$=2\times 2\times 2\times 3\times 4\times 9$

$=8\times 12\times 9$

$=96\times 9$

$=864$

$\therefore$ Required number $=$ L.C.M of $(24,32,36$ and $54$) $-5$

$=864-5=859$