Tougher questions in LCM

Find the greatest number less than 900 which is exactly divisible by 8, 12 and 28?

Answer:
LCM of 8,12, 28 = 168
to find the multiple of 168 = 900/168 =  5 60/168.
So, greatest number less than 900 which is exactly divisible = 900 - 60 = 840.

What greatest number can be subtracted from 2470 so that the Remainder may be divisible by 42, 98 and 105?

Answer:
Remainder will be LCM of 42, 98, 105 = 1470
So, the greatest number that can be subtracted = 2470 - 1470 = 1000.

Find the least number that being increased by 8 is divisible by 21, 35 and 48?

Answer:
LCM of 21, 35, 48 = 1680.
SO, the least number that being increased by 8 = 1680 -8 = 1672.

Find the least number which when divided by 18, 24, 30 and 42 will leave a remainder of 1 in each case.

Answer:
LCM of 18, 24, 30, 42 = 2520 
So, the least number that would leave a remainder of 1 = 2520 + 1 = 2521.