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

$\frak{Given}\begin{cases}& \sf{HCF\;of\;two\; Numbers =\frak{2}} \\ &\sf{LCM\;of\;two\;numbers=\frak{36}} \\ &\sf{One\;of \: the \: number\;is=\frak{18}}\end{cases}$

Need to find: The value of a?

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We're given with two numbers, the first number is 18. And, the other number is a.

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀⠀

$\bf{\bigstar}\;{ \underline{\boxed{\textsf{\textbf{\pink{Product of two Numbers = LCM \times HCF}}}}}}$ ⠀⠀

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$:\implies\sf a \times 18 = 2 \times 36 \\\\\\:\implies\sf a \times 18 = 72\\\\\\:\implies\sf a = \cancel\dfrac{72}{18}^{\;\;4} \\\\\\:\implies\underline{\boxed{\pmb{\frak{\pink{a = 4}}}}}\;\bigstar$

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$\therefore{\underline{\textsf{Hence, the required value of a is {\textbf{Option c) 4.}}}}}$

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$\rule{250px}{.3ex}$

$\qquad\quad\boxed{\underline{\underline{\purple{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

• HCF is (Highest common factor) which is the greatest factor b/w given any numbers.

• LCM is (Lowest common factor) which is the least number and LCM is exactly divisible by two or more numbers.

Answer 2

Answer:

Given :-

• The LCM of a and 18 is 36 and the HCF of a and 18 is 2.

To Find :-

• What is the value of a.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{Product\: of\: both\: number =\: HCF \times LCM}}}$

Solution :-

Since, it is given that first number is 18 and the other number is a.

Given :

$\mapsto$ H.C.F = 2

$\mapsto$ L.C.M = 36

According to the question by using the formula we get,

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

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

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

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

$\therefore$ The value of a is 4.

Hence, the correct options is option no (c) 4.

$\rule{150}{2}$

VERIFICATION :-

$\bigstar \sf Product\: of\: both\: number =\: H.C.F \times L.C.M$

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

By putting a = 4 we get,

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

$\implies \sf\bold{\purple{72 =\: 72}}$

Hence, Verified.

$\rule{150}{2}$

EXTRA INFORMATION :

$\clubsuit$ H.C.F :

• H.C.F full form is Highest Common Factor.
• H.C.F is also called Greatest Common Factor (GCF).

$\clubsuit$ L.C.M :

• L.C.M full form is Lowest Common Multiple.
• L.C.M is also called Least Common Divisor.