Page 167 - New Medley 5 Semester 1

C. Find the LCM of the following numbers using the common division method.
1. 18, 36 2. 20, 60 3. 25, 45 4. 16, 48, 72

5. 40, 75, 120 6. 63, 91, 130 7. 56, 84, 126 8. 120, 150, 210

Relationship between LCM, HCF and the Two given Numbers

Consider the numbers 12 and 18.

We have 12 = 2 × 2 × 3 and 18 = 2 × 3 × 3

∴ HCF = 2 × 3 = 6 and LCM = 2 × 2 × 3 × 3 = 36

Now, product of 12 and 18 = 12 × 18 = 216

and product of HCF and LCM = 6 × 36 = 216

Hence, we conclude that product of two numbers is the same as the
product of their HCF and LCM.

i.e., First number × second number = HCF × LCM

Using this formula, we can find any one out of four when three are given.

Example 8: The HCF and LCM of two numbers are 14 and 84
respectively. If one number is 28, find the other.

Solution: Given, HCF = 14, LCM = 84 and one number = 28

We know, First number × second number = HCF × LCM

HCF× LCM 14 ×84
So, second number = = = 42
First number 28

Word Problems Involving LCM and HCF

Example 9: There are 72 and 132 apples respectively kept in two
boxes. The apples are to be kept in rows, each row

containing equal number of apples. Find the maximum

number of apples that can be put in each row.

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