Question

HCF and LCM of two numbers are 48 and 384 respectively. IF one of the numbers is 192,find the other number.​

Answer 1

Answer:

96

Step-by-step explanation:

as product of 2 number =product of their hcf and lcm

so 192x=48*384

x=48*384/192

x=48*2

x=96

hope its helpful

Answer 2

• The other number = 96.

Given :

• The highest common factor (H.C.F.) of two numbers = 48.
• The least common multiple (L.C.M.) of two numbers = 384.
• The one number = 192.

To Find :

• The other number.

Solution :

Let,

The other number be x.

We know that,

H.C.F. × L.C.M. = One number × Other number

Given,

• The highest common factor (H.C.F.) = 48
• The least common multiple (L.C.M.) = 384
• One number = 192

⇒ 48 × 384 = 192 × x

⇒ 18432 = 192x

⇒ 18432 / 192 = x

⇒ 9216 / 96 = x

⇒ 4608 / 48 = x

⇒ 2304 / 24 = x

⇒ 1152 / 12 = x

⇒ 576 / 6 = x

⇒ 288 / 3 = x

⇒ 96 = x

∴ x = 96

Hence,

The other number is 96.

Verification :

H.C.F. × L.C.M. = One number × Other number

Now we have,

• The highest common factor (H.C.F.) = 48.
• The least common multiple (L.C.M.) = 384.
• One number = 192.
• Other number = 96.

⇒ 48 × 384 = 192 × 96

⇒ 18432 = 18432

Since, the value of both sides (R.H.S. and L.H.S.) are equal.

★ R.H.S. = L.H.S.

• R.H.S. = Right hand side.
• L.H.S. = Left hand side.

Hence Verified !