The Least Number!

Number Theory Level 2

Find the least number which is divisible by 126 , 168 126,168 and 147 147 perfectly (without leaving any remainder)


The answer is 3528.

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Krishna Ar by Krishna Ar , 21, India

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6 solutions

Aditya Raut
Jul 2, 2014

The answer is just the LCM of 126 , 168 and 147 \color{#20A900}{126} , \color{#3D99F6}{168} \text{ and } \color{#69047E}{147} , and

126 = 2 × 7 × 3 2 \color{#20A900}{126 = 2\times 7 \times 3^2}

168 = 2 3 × 3 × 7 \color{#3D99F6}{168 = 2^3 \times 3 \times 7}

147 = 2 × 7 2 \color{#69047E}{147 = 2\times 7^2}

Hence the LCM is 2 3 × 3 2 × 7 2 = 8 × 9 × 49 = 3528 \color{#D61F06}{2^3\times 3^2\times 7^2= 8\times 9\times 49 = \boxed{3528}}

14 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice coloring of numbers, haha XD

Jaydee Lucero - 6 years, 11 months ago

Nice solution...

Heder Oliveira Dias - 6 years, 11 months ago

How did you color the text of your solution?

Anik Mandal - 6 years, 11 months ago

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Use LaTeX \LaTeX codes as follows....

\color{Red}{Aditya} = A d i t y a \color{#D61F06}{Aditya}

\color{Green}{Raut} = R a u t \color{#20A900}{Raut}

\color{LimeGreen}{\text{Anik Mandal}} = Anik Mandal \color{limegreen}{\text{Anik Mandal}}

\color{Purple}{\Huge{Maths}} = M a t h s \color{#69047E}{\Huge{Maths}}

If you want the list of all latex color codes, here's the link for you my friend.... LaTeX colors for you

And in case if you say Thank You \color{#3D99F6}{\text{Thank You}} then You’re welcome \color{#D61F06}{\text{You're welcome}} in advance :P

Aditya Raut - 6 years, 11 months ago

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Thanks mate!

Anik Mandal - 6 years, 11 months ago

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@Anik Mandal – So now, reply to my comment in the new thing you learnt, reply me in a C O L O R F U L \color{#D61F06}{C} \color{#3D99F6}{O} \color{#20A900}{L} \color{limegreen}{O} \color{#69047E}{R} \color{#D61F06}{F} \color{#20A900}{U} \color{#3D99F6}{L} way :D

Aditya Raut - 6 years, 11 months ago

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@Aditya Raut – A n i k \color{#D61F06}{Anik} M a n d a l \color{#3D99F6}{Mandal}

A d i t y a \color{#20A900}{Aditya} R a u t \color{#CEBB00}{Raut}

Learnt to write colourfully! How's that? :)

Anik Mandal - 6 years, 11 months ago

2 * 7square is 98 !!

kavya goud - 6 years, 10 months ago

The answer is the LCM of 126,168 and 147,which is \color{midnightblue}{\text{The answer is the LCM of 126,168 and 147,which is}} 3528 \color{#D61F06}{\boxed{3528}}

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Jerald Junio
Nov 15, 2014

find the LCM of 126, 168, and 147. That's all

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Dinesh Grover
Oct 24, 2014

just find lcm

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Laxman Tiwari
Jul 25, 2014

a=126;b=168;c=147; r = (a b)/gcd(a,b); r = r c/gcd(r,c); and r is the answer

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........126,..168,..147
7.....|..18,.....24,....21
7.....|..18,.....24,....3
3.....|...18,....24,....1
3.....|.....6,......8
2.....|....2,.......8,
1.....|....1,........4,
7 * 7 * 3 * 3 * 2 * 4 = 3528






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