Question

find the least number which when divided by 5,6,7, and 8 leaves aremainder 3, but when divided by 9 leaves no remainder.

Answer 1

The number is 837.

Solution:

Question is to find the least common number.

Therefore find the lcm of 5,6,7,8.

LCM of 5,6,7,8= 840.

Now subtract the common remainder given(i.e. 3)

=840-3

=837.

Verification:

837/5 = 167 Remainder:2

837/6 = 139 Remainder:3

837/7 = 119 Remainder:4

837/8 = 104 Remainder:5

837/9 = 93 Remainder:0

All the remainders are given in the question itself. Therefore it verifies that the number is 837.

Trick to easily find LCM:

1. Find out the largest number from the given series.
2. Now find the multiples of that number. For example: In this problem largest number is 8, the multiples are 8,16,24 etc.
3. Check whether these multiples get completely divided by all the other numbers in the series.[(i.e.,) 8/5,8/6,8/7 etc.]
4. If the numbers doesn't completely divide the multiple, then go for the next multiple and redo the same method like,16/5,24/5,32/5 and so on till you get a multiple that gets completely divided by all other numbers.
5. In this problem, 840 is the LCM 840/5=168,840/6=140,840/7=120,840/8=105. Therefore the multiple gets completely divided by all the numbers.

Hope it helps you..