Question

If the lcm of two numbers is 216 and there product is 7776, what will be it's hcf

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\sf\underline{\blue{\:\:\:\: Given:-\:\:\:\:}}$

$\sf\bullet L.C.M\:of\: 2\: numbers=216\\ \\ \sf \bullet Their\: product=7776\\ \\ \sf\bullet Let\:H.C.F\:be\: x$

Now

$\boxed{\sf{L.C.M\times H.C.F=Product\:of\: numbers}}$

$\bf\underline{\red{\:\:\:\:A.T.Q:-\:\:\:\:}}$

$\sf\implies 216\times x=7776\\ \\ \sf\implies x=\cancel{\dfrac{7776}{216}}\\ \\ \sf\implies x=36\\ \\ \sf\implies So\:H.C.F=36$

• Let's verify

$\underline{\dag{\sf{\: Verification:-}}}$

$\sf\implies H.C.F\times L.C.M=Product\:of\: number's\\ \\ \sf\implies 216\times 36=7776\\ \\ \sf\implies 7776=7776\\ \\ \sf\:\:\:L.H.S=R.H.S\:\:(Hence\: verified!!)$

$\boxed{\bigstar{\sf{H.C.F=36}}}$

Answer 2

Solution

Given

• LCM of the two numbers is 216

• Product of the two numbers is 7776

To finD

• HCF of the two numbers

Let the two numbers be (a,b) and their HCF be y

Now,

$\huge{\boxed{\boxed{\tt HCF(a,b) \times LCM(a,b) = a \times b }}}$

Substituting the values,

$\leadsto \tt \: y \times 216 = 7776 \\ \\ \leadsto \: \sf \: y = \dfrac{7776}{216} \\ \\ \large{ \leadsto \: \boxed{ \boxed{ \tt \: y = 36}}}$

HCF of the two numbers is 36