Question

le GCD of two numbers is 17 and their LCM is 140. If one of the numbers is 20, find theother number. (3 marks)​

Answer 1

Question :–

GCD of two numbers is 17 and their LCM is 140. If one of the numbers is 20, find the other number.

Answer :–

• Other number is 119.

Given :–

• HCF = 17
• LCM = 140
• First number = 20

To Find :–

• Other number.

Solution :–

Let, the other number be x.

We know that,

★ H.C.F. × L.C.M. = Products of two numbers ★

→ 17 × 140 = 20 × x

→ 2,380 = 20x

→ 20x = 2,380

→ x = $\sf \frac{238 \cancel{0}}{2 \cancel{0}}$

→ x = $\sf \frac{\cancel{238}}{\cancel{2}}$

→ x = 119

Hence,

The other number is 119

Check :–

We know that,

★ H.C.F. × L.C.M. = Products of two numbers ★

→ 17 × 140 = 20 × 119

→ 2,380 = 2,380

Hence, both R.H.S. & L.H.S. are equal so it is correct ✔️

Answer 2

Let ,

The other number be " b "

Given ,

• HCF (20 , b) = 17
• LCM (20 , b) = 40

We know that , the relationship between LCM and HCF of two number a and b is given by

$\boxed{ \sf{HCF \: (a , b) = \frac{a \times b}{LCM \: (a , b)} }}$

Thus ,

$\sf \mapsto 17 = \frac{20 \times b}{140} \\ \\ \sf \mapsto b = 17 × 7 \\ \\ \sf \mapsto b = 119$

$\sf \therefore\underline{The \: other \: number \: is \: 119}$