Question

For each of the following pairs of numbers, verify that product of numbers is
equal to the product of their HCF and LCM.
(a) 10, 15
(b) 35, 40
(c) 32, 48​

Answer 1

1)10,15

10=2×5

15=3×5

LCM=2×3×5=30

HCF=5

Hence, LCM×HCF=30×5=150= Product of Numbers

2)35,40

35=5×7

40=2×2×2×5

LCM=5×7×8=280

HCF=5

Hence, LCM×HCF=280×5=1400 = Product of Numbers

3)32,48

32=2×2×2×2×2

48=2×2×2×2×3

LCM=96

HCF=16

Hence, LCM×HCF=96×16=1536 = Product of numbers

Answer 2

Answer:

(a) HCF X LCM = product of the 2 numbers

    10, 15 = HCF = 5

                 LCM = 30

                 HCF X LCM = 5 x 30

                                      = 150

                Product = 10 x 5

                              = 150

(b) HCF X LCM = product of the 2 numbers

    35, 40 = HCF = 5

                 LCM = 280

                 HCF X LCM = 5 x 280

                                      = 1400

                Product = 35 x 40

                              = 1400

(c) HCF X LCM = product of the 2 numbers

    32, 48 = HCF = 16

                 LCM = 96

                 HCF X LCM = 16 x 96

                                      = 1536

                Product = 32 x 48

                              = 1536