Question

Class:- 6
Chapter:- Factors and multiples

A) Find the L.C.M of the following by division method.
1) 112,160, 180
2) 25,40,60.

B) Find the prime factorization of 5000.

C) L.C.M can be determined by three methods:-
1) _____
2) _____
3) _____
Please answer correctly.​

Answer 1

Solution:-

A) Find the L.C.M of the following by division method.

1) 112 , 160 , 180

Answer:- 10080

Step-by-step explanation:-

$\begin{array}{r|l}\sf2&\sf112,160,180\\\cline{2-2}\sf2&\sf56,80,90\\\cline{2-2}\sf2&\sf28,40,45\\\cline{2-2}\sf2&\sf14,20,45\\\cline{2-2}\sf5&\sf7,10,45\\\cline{2-2}\sf7&\sf7,2,9\\\cline{2-2}\sf2&\sf1,2,9\\\cline{2-2}\sf9&\sf1,1,9\\\cline{2-2}&\sf1,1,1\end{array}$

Therefore, By using division method, L.C.M of the numbers is :-

= 2 × 2 × 2 × 2 × 5 × 7 × 2 × 9

= 10,080

2) 25,40,60

Answer:- 600

Step-by-step explanation:-

$\begin{array}{r|l}\sf2&\sf25,40,60\\\cline{2-2}\sf2&\sf25,20,30\\\cline{2-2}\sf5&\sf25,10,15\\\cline{2-2}\sf5&\sf5,2,3\\\cline{2-2}\sf5&\sf5,2,3\\\cline{2-2}\sf2&\sf1,2,3\\\cline{2-2}\sf3&\sf1,1,3\\\cline{2-2}&\sf1,1,1\end{array}$

Therefore, By using division method, L.C.M of the numbers is :-

= 2 × 2 × 5 × 5 × 2 × 3

= 600

B) Find the prime factorization of 5000.

Answer:-

$\begin{array}{r|l}\sf2&\sf5000\\\cline{2-2}\sf2&\sf2500\\\cline{2-2}\sf2&\sf625\\\cline{2-2}\sf5&\sf125\\\cline{2-2}\sf5&\sf25\\\cline{2-2}\sf5&\sf5\\\cline{2-2}&\sf1\end{array}$

By, using division method,

5000 = 2 × 2 × 2 × 5 × 5 × 5 × 5

C) L.C.M can be determined by three methods:-

1. Common Multiple method
2. Prime factorization method
3. Division method