Answer :

The smallest 3-digit number = 100

Since LCM of 6, 8, 12

$$
\begin{array}{|l}
\llap{2~~~~} 6 \\ \hline
\llap{3~~~~} 3 \\ \hline
1
\end{array}
$$
$$
\begin{array}{|l}
\llap{2~~~~} 8 \\ \hline
\llap{2~~~~} 4 \\ \hline
\llap{2~~~~} 2 \\ \hline
1
\end{array}
$$
$$
\begin{array}{|l}
\llap{2~~~~} 12 \\ \hline
\llap{2~~~~} 6 \\ \hline
\llap{3~~~~} 3 \\ \hline
1
\end{array}
$$
6= 2× 3

8 = 2× 2 × 2

12 = 2 × 2 × 3

Then LCM = 2 × 2 × 3 × 2 = 24

Now we need to find the smallest 3-digit multiple of 24

\(\therefore \) 24 × 4 = 96 and 24 × 5 = 120

Hence, 120 is the smallest 3-digit number which is exactly divisible by 6, 8 and 12

- Q.1. Renu purchases two bags of fertiliser of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the fertiliser exact number of times.
- Q.2 Three boys.step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm respectively. What is the minimum distance each should cover so that all can cover the distance in complete steps?
- Q.3 The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.
- Q.5 Determine the greatest 3-digit number exactly divisible by 8, 10 and 12.
- Q.6 The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?
- Q.7 Three tankers contain 403 litres, 434 litres and 465 litres of diesel respectively. Find the maximum capacity of a container that can measure the diesel of the three containers exact number of times.
- Q.8 Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case.
- Q.9 Find the smallest 4-digit number which is divisible by 18, 24 and 32.
- Q.10 Find the LCM of the following numbers: (a) 9 and 4 (b) 12 and 5 (c) 6 and 5 (d) 15 and 4 Observe a common property in the obtained ’ LCMs. Is LCM the product of two numbers in each case?
- Q.11 Find the LCM of the following numbers in which one number is the factor of the other. (a) 5, 20 (b) 6, 18 (c) 12, 48 (d) 9, 45 What do you observe in the results obtained?

- NCERT solutions for class 6 maths chapter 1 Knowing Our Numbers
- NCERT solutions for class 6 maths chapter 2 Whole Numbers
- NCERT solutions for class 6 maths chapter 3 Playing with Numbers
- NCERT solutions for class 6 maths chapter 4 Basic Geometrical Ideas
- NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes
- NCERT solutions for class 6 maths chapter 6 Integers
- NCERT solutions for class 6 maths chapter 7 Fractions
- NCERT solutions for class 6 maths chapter 8 Decimals
- NCERT solutions for class 6 maths chapter 9 Data Handling
- NCERT solutions for class 6 maths chapter 10 Mensuration
- NCERT solutions for class 6 maths chapter 11 Algebra
- NCERT solutions for class 6 maths chapter 12 Ratio and Proportion
- NCERT solutions for class 6 maths chapter 13 Symmetry
- NCERT solutions for class 6 maths chapter 14 Practical Geometry

- NCERT solutions for class 6 science chapter 1 Food: Where Does It Come From?
- NCERT solutions for class 6 science chapter 2 Components of Food
- NCERT solutions for class 6 science chapter 3 Fibre to Fabric
- NCERT solutions for class 6 science chapter 4 Sorting Materials into Groups
- NCERT solutions for class 6 science chapter 5 Separation of Substances
- NCERT solutions for class 6 science chapter 6 Changes Around us
- NCERT solutions for class 6 science chapter 7 Getting to Know Plants
- NCERT solutions for class 6 science chapter 8 Body Movements
- NCERT solutions for class 6 science chapter 9 The Living Organisms — Characteristics and Habitats
- NCERT solutions for class 6 science chapter 10 Motion and Measurement of Distances
- NCERT solutions for class 6 science chapter 11 Light, Shadows and Reflections
- NCERT solutions for class 6 science chapter 12 Electricity and Circuits
- NCERT solutions for class 6 science chapter 13 Fun with Magnets
- NCERT solutions for class 6 science chapter 14 Water
- NCERT solutions for class 6 science chapter 15 Air Around us