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example 1. The HCF and LCM of two numbers are 10 and 210, respectively. If one of the
numbers is 30, find the other number.

Solution. Given: HCF = 10, LCM = 210 and one number = 30
We know that: HCF × LCM = Product of the two numbers

Here, 10 × 210 = 30 × other number

2100 = 30 × other number

So, other number = 2100 ÷ 30 = 70.
Thus, the other number is 70.

example 2. The LCM of 90 and 120 is 360. Find their HCF.
Solution. Given that LCM = 360, and the two numbers are 90 and 120. 3 0
360 1 0 8 0 0
We know that: HCF × LCM = Product of the two numbers – 1 0 8 0

HCF × 360 = 90 × 120 0 0

HCF × 360 = 10800
HCF = 10800 ÷ 360 = 30

Thus, the HCF of 90 and 120 = 30.

Exercise 3f

1. Complete the following table.

HCF lCM Product of two numbers

a. 5 525

b. 11 66

c. 36 324

d. 20 120

2. Find the LCM of two numbers, if their product is 160 and the HCF is 4.

3. The HCF of two numbers is 5 and the LCM is 150. If one of the numbers is 25, find

the other.
4. The product of two numbers is 1350. Find their LCM if their HCF is 15.

5. If the LCM of two numbers is 120 and their product is 1800, what will be the HCF?

79
Multiples and Factors