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. (ii) 46, 51
(iii) 15, 60 ( (v) 78, 104​

Answer 1

Answer:

ii)HCF=1,LCM=2346

iii)HCF=15,LCM=60

iv)HCF=26,LCM=312

Step-by-step explanation:

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)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.

Hope it helps you....