Let us find the HCF and the LCM of 36 and 48. First, find the factors of 36 and 48 using division method.

**Relationship
between the Numbers and their HCF and LCM**

Let us find the HCF and the LCM of 36 and 48. First,
find the factors of 36 and 48 using division method.

36
= 2 × 2 × 3 × 3;

48
= 2 × 2 × 2 × 2 × 3

HCF
= 2 × 2 × 3 = 12

LCM
= 2 × 2 × 3 × 2 × 2 × 3 =144

Observe
that, 36 × 48 = 144 × 12 = 1728

We find that,

**product of two given numbers = their
HCF × LCM**

In general, for any 2 numbers *x* and *y*,

*x ***× y= HCF (x, y) ×**

** **

__Example 12: __

The LCM of two numbers is 432 and their
HCF is 36. If one of the**
**numbers is 108, then find the other
number.

**Solution:** We know that, the product of the two numbers=LCM
× HCF

108 × (the other number) = 432 × 36

The other number = (432 × 36) ÷ 108 = 144

** **

__Example 13: __

The LCM of two co-prime numbers is 5005.
If one of the numbers is 65,**
**then find the other number.

**Solution:** We know that, the product of the two numbers = LCM
× HCF

As the HCF of co-primes is 1,

65
× (the other number) = 5005 × 1

The
other number = 5005 ÷ 65 = 77

**NUMBERS**

**ICT CORNER**

**Expected Outcome**

**Step 1**

Open the Browser and type the URL Link
given below (or) Scan the QR Code. GeoGebra work sheet named “Numbers” will open.
The work sheet contains two activities. 1. LCM and HCF and 2. Prime number game.

In the first activity Click on New Problem
and solve the problem, then check your answer.

**Step 2**

In the second activity catch the egg
which shows prime number as quick as possible. You can select the level of speed
in the beginning.

**Browse in the link:**

Numbers: __https://ggbm.at/Exu3mtz5__
or Scan the QR Code.

Tags : Numbers | Term 2 Chapter 1 | 6th Maths , 6th Maths : Term 2 Unit 1 : Numbers

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

6th Maths : Term 2 Unit 1 : Numbers : Relationship between the Numbers and their HCF and LCM | Numbers | Term 2 Chapter 1 | 6th Maths

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