# LCM Questions and Answers - Form 1 Topical Mathematics

## Questions

1. A piece of land is to be divided into 20 acres or 24 acres or 26 acres or 28 acres for farming and leave 7 acres for grazing. Determine the smallest size of such land.
2. When a certain number x is divided by 30, 45 or 54, there is always a remainder of 21. Find the least value of the number x
3. A number m is such that when it is divided by 30, 36, and 45, the remainder is always 7. Find the smallest possible value of m.
4. Find the L.C.M of x2 + x , x2 – 1 and x2 – x

1.
 2 20 24 26 28 2 10 12 13 14 2 5 6 13 7 3 5 3 13 7 5 5 1 13 7 7 1 1 13 7 13 1 1 13 1 1 1 1 1 1

Size of the land = ((23 x 3 x 5 x 7 x 13) + 7) acres
= 10920 + 7 = 10,927 acres
2.  2 30 45 54 3 15 45 27 3 5 15 9 3 5 5 1 5 5 5 1 1 1 1 1
Least value of x = (2 x 33 x 5) + 21
=270 + 21 = 291
3.  2 30 36 45 2 15 18 45 3 15 9 45 3 5 3 15 5 5 1 5 1 1 1
Smallest value of m = (22 x 33 x 5) + 7 = 187
4. x2 + x = x (x + 1)
x2 -1 = (x + 1) (x – 1)
x2 – x = x(x – 1)
x(x+1) (x – 1)
x3- x

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