Question

Find the least number which when
divided by 20,25, 35 and 40 leaves
remainder 14, 19, 29 and 34 respectively
(plz answer fast)​

Answer 1

Tᴏ Fɪɴᴅ :-

• The least number which when divided by 20,25, 35 and 40 leaves remainder 14, 19, 29 and 34 respectively...

ᴄᴏɴᴄᴇᴘᴛ ᴜsᴇᴅ :-

In case we have to Find the least no. which when divided by x, y and z leaves the remainders a, b and c respectively.

Then, it is always observed that :-

☞ (x - a) = (y - b) = (z - c) = K (say).

∴ Required no. = {(L.C.M. of x, y and z) - K}.

Sᴏʟᴜᴛɪᴏɴ :-

⟿ (20 - 14) = (25 - 19) = (35 - 29) = (40 - 34) = 6 = k .

Now, LCM of (20,25,35,40) :-

⟿ 20 = 2 * 2 * 5 = 2² * 5

⟿ 25 = 5 * 5 = 5²

⟿ 35 = 5 * 7

⟿ 40 = 2 * 2 * 2 * 5 = 2³ * 5

LCM = 5² * 7 * 2³ = 25 * 7 * 8 = 1400 .

Therefore,

⟿ Required No. = LCM of (20,25,35,40) - k

⟿ Required No. = 1400 - 6

⟿ Required No. = 1394 (Ans.)

Hence, The Required Least Number is 1394.

Answer 2

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

${\bf{\blue{\underline{To\:Find:}}}}$

• Least number which when divided by 20,25,35 and 40 leaves remainder 14,19,29 and 39 respectively.

${\bf{\blue{\underline{Now:}}}}$

• Common Value = Number - Remainder

$\longrightarrow{\sf{ 20 - 14 = 6}}$

$\longrightarrow{\sf{ 25 - 19 = 6}}$

$\longrightarrow{\sf{ 35 - 29 = 6}}$

$\longrightarrow{\sf{ 40 - 34 = 6}}$

__________________________________

Here L.C.M of given number is

$: \implies{\sf{ 20 = {2}^{2} \times 5 }}$

$: \implies{\sf{ 25 = {5}^{2} }}$

$: \implies{\sf{ 35 = 7 \times 5 }}$

$: \implies{\sf{ 40 = {2}^{3} \times 5 }}$

Therefore L.C.M is,

$: \implies{\sf{ L.C.M= {2}^{3} \times {5}^{2} \times 7 =1400}}$

___________________________________

Hence, the required answer is

• 1400- 6 = 1394.