Question

2. Find the HCF and LCM of the numbers given below. Verify that their product is
equal to the product of the given numbers.
(i) 32, 37
(ii) 46, 51 (iii) 15, 60 (iv) 18, 63 (v) 78, 104



standard 7 ​

Answer 1

Answer:

Find the HCF and LCM of the number given below. Verify that their product is equal to the product of the given numbers. 32,37 ?

Answer 2

Step-by-step explanation:

32 = 2 x 16  = 2 x 2 x 8  = 2 x 2 x 2 x 4  = 2 x 2 x 2 x 2 x 2 x 1  37 = 37 x 1  ∴ HCF of 32 and 37 =1  LCM of 32 and 37 = 2 x 2 x 2 x 2 x 2 x 37  = 1184 HCF x LCM = 1 x 1184  = 1184  Product of the given numbers = 32 x 37  = 1184  ∴ HCF x LCM = Product of the given numbers.  ii. 46 = 2 x 23 x 1  51 = 3 x 17 x 1

  ∴ HCF of 46 and 51 = 1  LCM of 46 and 51 = 2 x 23 x 3 x 17  = 2346  HCF x LCM = 1 x 2346  = 2346 Product of the given numbers = 46 x 51  = 2346  ∴ HCF x LCM = Product of the given numbers

iii. 15 = 3 x 5  60 = 2 x 30  = 2 x 2 x 15  = 2 x 2 x 3 x 5  ∴ HCF of 15 and 60 = 3 x 5  = 15  LCM of 15 and 60 = 3 x 5 x 2 x 2  = 60  HCF x LCM = 15 x 60  = 900  Product of the given numbers = 15 x 60  = 900  ∴ HCF x LCM = Product of the given numbers.

iv. 18 = 2 x 9  = 2 x 3 x 3  63 = 3 x 21  = 3 x 3 x 7  ∴ HCF of 18 and 63 = 3 x 3 = 9  LCM of 18 and 63 = 3 x 3 x 2 x 7  = 126  HCF x LCM = 9 x 126  = 1134  Product of the given numbers = 18 x 63  = 1134  ∴ HCF x LCM = Product of the given numbers. 

v. 78 = 2 x 39  = 2 x 3 x 13 104  = 2 x 52  = 2 x 2 x 26  = 2 x 2 x 2 x 13  ∴ HCF of 78 and 104 = 2 x 13  = 26  LCM of 78 and 104 = 2 x 13 x 3 x 2 x 2  = 312  HCF x LCM = 26 x 312 = 8112  Product of the given numbers = 78 x 104  = 8112  ∴ HCF x LCM = Product of the given numbers.

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