2. 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
Answers
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
HCF (14, 21) = 7
LCM (14, 21) = 2 × 3 × 7 = 42
HCF × LCM = Product of numbers
↠ 7 × 42 = 14 × 21
↠ 294 = 294
Hence, Verified
(ii) 27, 90
By using prime factorisation method.
- Factors of 27 = 3³
- Factors of 90 = 2 × 3² × 5
HCF (27, 90) = 3² = 9
LCM (27, 90) = 2 × 3³ × 5 = 270
HCF × LCM = Product of numbers
↠ 9 × 270 = 27 × 90
↠ 2430 = 2430
Hence, Verified
Given :-
(i) 14,21
(ii) 27,90
To Find :-
For each of the following pairs of numbers, show that the product of their HCF and LCM equals their product:
Solution :-
(i) 14,21
Factor of 14 = 1, 2, 7, 14
Factor of 21 = 1, 3, 7, 21
Common factor = 1,7
HCF = 7
Multiple of 14 = 14, 28, 42
Multipe of 21 = 21, 42
LCM = 42
Now
a × b = HCF × LCM
14 × 21 = 7 × 42
294 = 294
(ii) 27, 90
Factor of 27 = 1, 3, 9, 27
Factor of 90 = 1, 2, 3, 5, 9, 10, 18, 30, 45, 90
Common factor = 1,3,9
HCF = 9
Multiple of 27 = 27, 54, 81, 108, 135, 162, 189, 216, 243, 270
Multiple of 90 = 90, 180, 270
LCM = 270
a × b = HCF × LCM
27 × 90 = 9 × 270
2430 = 2430