Question

For each of the following pairs of numbers show that the product of their HCF and LCM equals their product:
(i) 14,21
(ii) 27,90

Answer 1

Answer:

I) HCF of 14 and 21 is7

LCM of 14 and 21 is 42

We know that LCM × HCF = product of 2 numbers

So, 14×21=7×42

=294

HCF of 27 & 90 is9

LCM of 27& 90 is 270

Similarly,

27×90=9×270

=243

Answer 2

Question:

• For each of the following pairs of numbers, show that the product of their HCF and LCM equals their product:

(i) 14, 21

By using prime factorisation method.

• Factors of 14 = 2 × 7
• Factors of 21 = 3 × 7

$\dashrightarrow$HCF (14, 21) = 7

$\dashrightarrow$LCM (14, 21) = 2 × 3 × 7 = 42

HCF × LCM = Product of numbers

↠ 7 × 42 = 14 × 21

↠ 294 = 294

$\huge\bold{Hence, Verified}$

(ii) 27, 90

By using prime factorisation method.

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

$\dashrightarrow$HCF (27, 90) = 3² = 9

$\dashrightarrow$LCM (27, 90) = 2 × 3³ × 5 = 270

HCF × LCM = Product of numbers

↠ 9 × 270 = 27 × 90

↠ 2430 = 2430

$\huge\bold{Hence, Verified}$