Question

show the product of LCM and HCF of 18 and 90 is equal to their product​

Answer 1

Answer:

L.C.M is 90

H.C.F is 18

the product is 90*18=1620

and it is equals to L.C.M*H.C.F

Answer 2

Solution:

Let 'p' be 18

Let 'q' be 90

Step 1: Finding the HCF of 18 and 90.

18 $\longrightarrow$ 2 × 3²

90 $\longrightarrow$ 2 × 3² × 5

$\rule{200}{1}$

HCF $\longrightarrow$ 2 × 3²

HCF $\longrightarrow$  2 × 9

∴ HCF $\longrightarrow$  18

Step 2: Finding the LCM of 18 and 90.

18 $\longrightarrow$ 2 × 3²

90 $\longrightarrow$ 2 × 3² × 5

$\rule{200}{1}$

LCM $\longrightarrow$ 2 × 3² × 5

LCM $\longrightarrow$ 2 × 9 × 5

∴ LCM $\longrightarrow$ 90

Step 3: Proving that the Product of the LCM and HCF is equal to the product of the numbers.

p × q = LCM(18, 90) × HCF(18, 90)

18 × 90 = 90 × 18

1620 = 1620

LHS = RHS

Hence Proved.