Question

find the least 5 digit number which is exactly divisible by 20,25 and 30.​

Answer 1

$\red{\boxed{\boxed{AMSWER:-}}}$

Decompose each into prime factors.

20 = 2*2*5

25 = 5*5

30 = 2*3*5

Lowest common multiple is then

2*2*3*5*5 = 300

Now you need the lowest number so that

300 * N >= 10000

then

N >= 10000/300

N > 33.3…

Being N an integer, N has to be 34.

300 * 34 = 10200

Answer 2

★ Question ★

$\rule{300}2$

→ find the least 5 digit number which is exactly divisible by 20,25 and 30.

$\rule{300}2$

if the number is divisible by 20,25,30 it mean the product of the L,C,M.

so,

l.c.m of 20,25,30= 300

we know that smallest 5 digit number = 10,000

now,

10,000 is not completely divisible by 300 = 33.33

so,

check 10200 is completely divisible by 300

10,200÷300 = 34

again checking 10,200 is divisible by 20,25,and 30

10,200÷ 20 = 510

10,200÷25=408

10,200÷30 = 340

so,

The least 5 digit number ( 10,200 ) exactly divisible by 20,25 and 30.

$\rule{300}2$