Determine the greatest 3-digit number exactly divisible by 8, 10 and 12

Solution:

We will be using the concept of LCM(Least Common Multiple) to solve this.

To determine the greatest 3-digit number exactly divisible by 8, 10, and 12, we need to find the LCM of the given numbers.

Let's find the LCM of 8, 10, and 12 as shown below.

LCM of 8, 10, and 12 will be equal to 2 × 2 × 2 × 3 × 5 = 120

As we know that the greatest 3-digit number is 999, we will now divide 999 by the obtained LCM that is 120.

Since the remainder is not 0, hence we subtract 39 from 999.

999 - 39 = 960 which is a multiple of 120 and is exactly divisible.

Now,

120 × 8 = 960 and 120 × 9 = 1080.

We see that 120 × 9 = 1080 is a 4-digit number but, we need the greatest 3-digit multiple.

Therefore, the greatest 3-digit multiple of 120 is 120 × 8 = 960 i.e, 960.

Hence, the greatest 3-digit number exactly divisible by 8, 10, and 12 is 960.

You can also use the LCM Calculator to solve this.

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.7 Question 5

Determine the greatest 3-digit number exactly divisible by 8, 10 and 12

Summary:

The greatest 3-digit number exactly divisible by 8, 10, and 12 is 960.

☛ Related Questions:

• 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 Am At What Time
• 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
• Find The Least Number Which When Divided By 6 15 And 18 Leave Remainder 5 In Each Case
• Find The Smallest 4 Digit Number Which Is Divisible By 18 24 And 32