Question

FIND THE LCM BY PRIME FACTORISATION METHOD THE NUMBER IS 64,80,100
[PLEASE ANSWER AND ALSO EXPLAIN]

Answer 1

★ Solution :-

$\setlength{\unitlength}{1mm}\begin{picture}(0,0)\put(0,0){\begin{array}{c|c}2&64\\\cline{1-2} 2&32 \\\cline{1-2}2&16\\\cline{1-2}2&8\\\cline{1-2}2&4\\\cline{1-2}2&2\\\cline{1-2}&1\end{array}} \put(20,2){\begin{array}{c|c}2&80\\\cline{1-2}2&40\\\cline{1-2}2&20\\\cline{1-2}2&10\\\cline{1-2}5&5\\\cline{1-2}&1\end{array}}\put(40,4){\begin{array}{c|c}2&100\\\cline{1-2}2&50\\\cline{1-2}5&25\\\cline{1-2}5&5\\\cline{1-2}&1\end{array}} \put(0,-22){64=2\times2\times2\times2\times2\times2}\put(0,-27){80=2\times2\times2\times2\times5}\put(0,-31){100=2\times2\times5\times5}\end{picture}$

Now , taking prime factors of 64 , 80 & 100

Prime factors (64) :- 2 , 2 , 2 , 2 , 2 , 2

Prime factors (80) :- 2 , 2 , 2 , 2 , 5

Prime factors (100) :- 2 , 2 , 5 , 5

Now , taking common & multiplying

→ 2 × 2 × 2 × 2 × 2 × 2 × 5

→ 64 × 5

→ 320

Hence , LCM of 64 , 80 & 100 is 320.

Answer 2

LCM of 64 , 80 , 100 is 1600

Given :

The numbers 64 , 80 , 100

To find :

LCM by prime factorisation

Concept :

LCM :

For the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

Solution :

Step 1 of 3 :

Write down the given numbers

The given numbers are 64 , 80 , 100

Step 2 of 3 :

Prime factorise the given numbers

64 = 2 × 2 × 2 × 2 × 2 × 2

80 = 2 × 2 × 2 × 2 × 5

100 = 2 × 2 × 5 × 5

Step 3 of 3 :

Find LCM

The required LCM

= 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5

= 1600

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