Question

Question 11

Find the LCM of the following numbers in which one number is the factor of other:
(a) 5, 20 (b) 6, 18 (c) 12, 48 (d) 9, 45
What do you observe in the result obtained?

Answer 1

The least common multiple (LCM) of 2 or more numbers is the smallest number that they all divide evenly.

(a) $\begin{array}{cc}2& 5,20\\ 2& 5,10\\ 5& 5,5\\ & 1,1\end{array}$

LCM of 5 and 20
= $2\times 2\times 5$
= 20

(b) $\begin{array}{cc}2& 6,18\\ 3& 3,9\\ 3& 1,3\\ & 1,1\end{array}$

L.C.M. of 6 and 18
= $2\times 3\times 3$
= 18

(c) $\begin{array}{cc}2& 12,48\\ 2& 6,24\\ 2& 3,12\\ 2& 3,6\\ 3& 3,3\\ & 1,1\end{array}$

L.C.M of 12 and 48
= $2\times 2\times 2\times 2\times 3$
= 48

(d) $\begin{array}{cc}3& 9,45\\ 3& 3,15\\ 5& 1,5\\ & 1,1\end{array}$

L.C.M. of 9 and 45
= $3\times 3\times 5$
= 45

From these all cases, we can conclude that if the smallest number if the factor of the largest number, then the LCM. of two numbers is equal to that of the larger number.