Question 10 (a)

Find the LCM of the following numbers:
9 and 4
Observe a common property in the obtained LCMs. Is LCM the product of two numbers in each case?

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Solution

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

$\begin{matrix} 2 & 9, 4 2 & 9, 2 3 & 9, 1 3 & 3, 1 1, 1 \end{matrix}$

LCM of 9 and 4
= $2 \times 2 \times 3 \times 3$
= 36
Yes, the LCM is equal to the product of two numbers in this case because both 9 and 4 do not have any common factor. And LCM is also the multiple of 3.

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Question 10 (d)

Find the LCM of the following numbers:
15 and 4
Observe a common property in the obtained LCMs. Is LCM the product of two numbers in each case?

Find the LCM of the following numbers:

(a) 9 and 4 (b) 12 and 5

Observe a common property in the obtained LCMs. Is LCM the product of two numbers in each case?

Question 2 (i)
Find the LCM and HCF of 26, 91 and verify that LCM $\times$ HCF = product of the two numbers.

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