Question

The hcf and lcm of two numbers are 12 and 5040 respectively, if one of the numbers is 144 find the other number.

Answer 1

Gɪᴠᴇɴ :-

• H. C. F = 12
• L. C. M = 5040
• One number = 144

ᴛᴏ ғɪɴᴅ :-

• Other Number

sᴏʟᴜᴛɪᴏɴ :-

We know that,

➢ Product of two numbers = H. C. F × L. C. M

On putting above given values in it, we get,

➭ n1 × n2 = H. C. F × L. C. M

➭ 144 × n2 = 12 × 5040

➭ 144 × n2 = 60480

➭ n2 = 60480/144

➭ n2 = 420

Hence,

• Other Number is 420

➢ᴠᴇʀɪғɪᴄᴀᴛɪᴏɴ :-

Product of two numbers = H. C. F × L. C.M

➭ n1 × n2 = H. C. F × L. C. M

➭ 144 × 420 = 12 × 5040

➭ 60480 = 60480

➭ L.H.S = R.H.S

Hence verified...

Answer 2

GIVEN:

• H.C.F and L.C.M of twi numbers are 12 and 5040 respectively.

• If one of the number is 144

TO FIND:

• The other number.

SOLUTION:

Let the other number be x

As we know that,

Product of two numbers = H.C.F × L.C.M

=> x × 144 = 12 × 5040

=> x = (12 × 5040)/144

=> x = 5040/ 12

=> x = 420

Therefore, The other number be 420