Question

Determine the smallest 3 digit number whichis exactly divisible by 6, 8 and 12

Answer 1

if the digit is divided by 12 it is automatically divided by 6 because 12=6*2
so now we need to find a 3digit number divided by 12 and 8
lcm=24
smallest 3 digit no. is 100
divide 100 by 24 and subtract the remainder from 24 and add in 100 remainder=4,24-4=20
100+20=120

Answer 2

To find Smallest n-digit no. which when divided by x,y and z leaves no remainder (i.e., exactly divisible by x,y and z)

Approach:
1.Find LCM of x,y and z (Say L)
2.Divide smallest n-digit no. by L and note value of remainder 'R'
Required No. = n-digit smallest no. +(L-R)

==========×××××××××==========

Smallest 3 digit no. = 100
LCM of 6,8 and 12 = 2³*3 = 24

100/3 Remainder,R=1
Required No. = 100+(24-4)=120


Verification:
120/6= 20
120/8= 15
120/12= 10


Hope it helps
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