Question

the product of 2 numbers is 20736,HCF is 34,find LCM​

Answer 1

$\huge\bf{\underline{\red{Solution:-}}}$

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

$\sf\bullet H.C.F\:of\:2 \: numbers=34\\ \\ \sf\bullet Their\: product 20736\\ \\ \sf\bullet LC.M= ?\\ \\ \sf\:\:\:\:\:\:{\scriptsize{\dag{Now\:we\:have\:to\: find\:L.C.M}}}$

$\sf\bullet \:\:Let\:the\:L.C.M\:\:be\:\: x$

Now

$\sf\:\:\:we\:know\:\:that$

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

So

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

$\sf\:\:\:H.F.C\times L.C.M=Product\:of\: numbers\\ \\ \sf\:\:\:\:\:Put\:the\:value\\ \\ \sf\implies 34\times x=. 20736\\ \\ \sf\implies x=\cancel{\dfrac{20736}{34}}\\ \\ \sf\implies x= 609.88 \:\:(approx)$

$\sf{\blue{\:\:L.C.M\:= 609.88}}$

$\large\bf{\underline{\red{Verify:-}}}$

$\sf{\scriptsize{\dag{H.C.F\times L.C.M=Product\:of\: numbers}}}\\ \\ \sf\implies 34\times 609.88=20736\\ \\ \sf\implies 20735.92=20736\\ \\ \sf \:\:\:L.H.S=R.H.S$

Answer 2

Answer:

$\large{\underline{\boxed{\mathfrak\blue{LCM = 610 \: \: \: [Approx.]}}}}$

Question:-

The product of 2 numbers is 20736.HCF is 34,Find LCM.

Given:-

• Product of numbers = 20736

• HCF = 34

To find:-

• LCM = ?

$\rm We \: know, \\\\ {\boxed{\rm{Product \: of \: numbers = HCF \times LCM }}}$

$→ \sf 20736 = 34 \times LCM \\\\ → \sf 20736 = 34LCM \\\\ → \sf LCM = \dfrac{20736}{34} \\\\ →\sf LCM = 609.88 \\\\ → \large{\underline{\boxed{\sf\blue{LCM \approx 610 }}}}$

To verify:-

$LCM \times HCF = Product \: of \: numbers \\\\ ⇒ 609.88 \times 34 = 20736 \\\\ ⇒ 20736 = 20736 \: \: \: \: [Approx.] \: \:[Verified!]$

$\therefore\sf\green{LCM \approx 610}$