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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

1 Answer

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i. 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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