Question

Two numbers are in the ratio 2:3
and their HCF is 13. Find the LCM of those two numbers.​

Answer 1

$\mathtt{\huge{\underline{\orange{Answer :-}}}}$

➝ $\dfrac{6x}{13}$

$\mathtt{\huge{\underline{\pink{Explanation :-}}}}$

$\sf{\huge{\underline{\red{Given :-}}}}$

• Two numbers are in the ratio 2:3 and their HCF is 13.

$\sf{\huge{\underline{\green{To\:Find:-}}}}$

• The LCM of those two numbers.

$\sf{\huge{\underline{\blue{Solution :-}}}}$

We know that ,

The product of two numbers are (HCF of the two numbers) x (LCM of the two numbers)

➝ 2x × 3x = 13 × LCM

➝ 6x = 13 × LCM

➝ LCM = $\dfrac{6x}{13}$

$\sf{\huge{\underline{\purple{Verification :-}}}}$

2x × 3x = 13 × LCM

➝ 6x = 13 × $\dfrac{6x}{13}$

➝ 6x = 6x

Hence, Verified .

________________________________

Answer 2

Answer:

Let the two numbers be 2x and 3x respectively.

The HCF of 2x and 3x is x.

⇒ x = 13

We know that,

Product of two numbers x and y = LCM(x, y) × HCF(x, y)

⇒ 2× 13 × 4 × 13 = LCM × 13

⇒ LCM = 78

∴ LCM = 78