Question

If the LCM of a and 18 is 36 and the HCF of a and 18 Is 2, then what is the value of a?

(a) 2 (b) 3 (c) 4 (d) 1​

Answer 1

Answer:

Answer: The value of a is 4.

Let's find the value of a

Explanation:

Given that, LCM(a, 18) is 36 and HCF(a,18) is 2. One of the numbers is known to us as 18.

So, by applying the formula: LCM × HCF = a × 18

36 × 2 = a × 18

72 = 18(a)

18a = 72

a = 72/18 = 4.

Hence, the value of a is 4.

Answer 2

$\bf \underline{Given }:$ ↴

$\sf \implies \: LCM \: of \: 2 \: numbers = 36$

$\sf \implies \: HCF \: of \: two \: numbers = 2$

$\sf \implies \: One \: of \: the \: number = 18$

$\bf \underline{To \: find}:$ ↴

$\sf \implies \: The \: value \: of \: a$

$\bf \underline{Formula \: to \: be \: used \: here},$

$\boxed{ \pink{\sf Product \: of \: two \: numbers = LCM \times HCF }}$

$\bf \underline{\underline{Solution}}$

$\sf Putting \: the \: values,$

$\sf \implies a \times 18 = 2 \times 36$

$\sf \implies a \times 18 = 72$

$\sf \implies 18a = 72$

$\sf \implies a = \dfrac{18}{72}$

$\red{\sf \implies a = 4}$

$\underline{ \boxed{ \pink{\sf Therefore, the \: values \: of \: a = 4 }}}$

________________________________

$\bf \underline{Let's \: verify \: our \: answer},$

To verify your answer we will put the value of a (4) into the formula.

$\sf \implies 4 \times 18 = 2 \times 36$

$\sf \implies 72 = 72$

$\red{ \bf \: Hence \: verified \: ! }$

________________________________

$\bf \underline{More \:to \:know} \: !$

LCM stands for Lowest common factor. It is the least number and LCM is exactly divisible by two or more numbers.

HCF stands for Highest common factor. It is the greatest factor between given any numbers.