Question

✦✧✧ Question ✧✧✦ ➠ ᴅᴏɴᴛ sᴘᴀᴍ⚠️ correct answer will surely get brillianist​ Find the smallest number which when decreased by 11 is exactly divisible by both 420 and 168.​

Answer 1

$\sf\huge\bold{Answer:}$

Given :

Numbers → 420 and 168

To find :

the smallest number which when decreased by 11 is exactly divisible by both 420 and 168.

Solution :

To find the least number, we need to find the LCM of 420 and 168

$\: \: \: 2 \: \: |420 - 168\\ - - | - - - - - \\ \: \: \: \: \: 2 \: \: |210 - 84 \: \: \: \: \: \\ - - | - - - - - \\ \: \: \: 2 \: \: \: | 105 - 42\: \: \: \: \\ - - | - - - - - \\ \: 3 \: \: \: |105 - 21 \: \: \\ - - | - - - - - \\ \: \: 5 \: \: \: |35 - 7 \:\:\: \: \: \: \: \: \\ - - | - - - - - \\ \: \: 7 \: \: \: |7 - 7 \: \:\: \:\: \: \: \: \: \: \\ - - | - - - - - \\ \: \: \: \: \: \: \: |1 - 1\: \:\: \: \:\: \: \: \: \:$

Least Common Factor (LCM) of 420 and 168 = 2³×3×5×7

= 2×2×2×3×5×7 = 840

Decrease 840 by 11 = 840-11 = 829

Hence, 829 is the smallest number which when decreased by 11 is exactly divisible by both 420 and 168.

$\sf\huge\purple{829}$

Answer 2

Answer:

Here is your answer buddy,

Step-by-step explanation:

Question,

Find the smallest number which when decreased by 11 is exactly divisible by both 420 and 168.

Answer,

Points that we should know,

• $LCM \: (\: least \: common \: multiple\: )$

• $If\: a\: ,\: b \: are\: two \: integers\:, \\ Lcm \: is\: the\: least\: common\: multiple\: \\of \: a\: ,\: b$

How to find LCM,

• $By\: Listing \: multiples\:$

• $Prime\: factorisation \:$ etc...

LCM of 420 and 168 by listing multiples

420 multiples =

• 420, 840, 1260, 1680, 2100,2520, 2940, 3360, 3780,4200etc..

168 multiples =

• 168, 336, 504, 672, 840, 1008, 1176, 1344, 1512, 1680, 1848 etc...

$Now \: take \: 420 \: as \: reference\: as \: it \: is \: the \: \\ big \: number$

$Observe \: every \: multiple \: of \: 420 \: that \: \\ whether \: it \: is \: the \: multiple \: of \: 168 \: or \: not$

$We \: can \: see \: 840 \: , \: 1680 \: are \: the \: common \: \\multiples \: in \: our \: list$

Therfore,

$least \: common \: multiple \: is \\\: 840$

LCM of 420 and 168 by prime factorisation,

2$\: \:$ | 420 , 168

$\:\: \: \:$ ---------------

2$\: \:$ | 210 , 84

$\: \: \: \:\:$ ---------------

3 $\:\:$ | 105 , 42

$\:\: \: \: \:$ ---------------

7 $\: \:$ | 35 , 14

$\: \: \: \:\:$ ---------------

5 $\:\:$ | 5 , 2

$\:\: \: \: \:$ ---------------

2$\:\:$ | 1 , 2

$\: \:\: \: \:$ ---------------

$\:\: \:\: \:$ | 1 , 1

LCM OF 420 AND 168

$\: \: \: \: \: \: \: \: \:$ = 2 × 2 × 2 × 3 × 7 × 5

$\: \: \: \: \: \: \: \:$ = 840

So, we found that LCM OF 420 and 168 is 840

Solution,

A number decreased by 11 will be the smallest divisible number of 420 and 168

Let the number be X,

X - 11 is th smallest divisible number of 420 and 168

X - 11 = LCM OF 420 AND 168

X - 11 = 840

X = 840 + 11

X = 851

SO, THE REQUIRED NUMBER IS 851

(TO FIND LCM USE PRIME FACTORIZATION METHOD FOR TIME SAVING AND IT IS THE EASY WAY )

HAVE A GOOD DAY ❤️