Question

For the given pairs of numbers show that the product of their h.c.f and l.c.m equals their products 27 and 90

Answer 1

Given :-

Two numbers 27 and 90

To Find :-

Verify that their product is equal to the product of HCF and LCM

Solution :-

At first we need to find HCF and LCM of 27 and 90

By using prime factorizing method

Factor of 27

3|27

3|9

3|3

1

Factors = 3 × 3 × 3 × 1

Factor of 90

2|90

3|45

3|15

3|5

5

Factors = 2 × 3 × 3 × 3 × 5

Now

HCF = 3 × 3 = 9

LCM = 2 × 3 × 3 × 3 × 5 = 270

Verification

HCF × LCM = a × b

9 × 270 = 27 × 90

2430 = 2430

Answer 2

Given numbers:

• 27 and 90

To show:

• The product of their HCF and LCM equals their products.

Finding their HCF and LCM:

Using prime factorisation.

• Factors of 27 = 3³
• Factors of 90 = 2 × 3² × 5

HCF (27, 90) = 3² = 9

LCM (27, 90) = 2 × 3³ × 5 = 270

Product of HCF and LCM:

↠ HCF × LCM = 9 × 270

↠ HCF × LCM = 2430

Product of 27 and 90:

↠ 27 × 90 = 2430

Here, 2430 = 2430

i.e., Product of HCF and LCM = Product of given pairs of numbers

Hence,

• Proved.