Question

(a)Find the LCM of 9,15 and 18(b)9 divides into LCM___times15 divides into LCM__times18 divides into LCM___times

Answer 1

(a)90

(b)(i) 10 (ii)6 (iii)5

Step-by-step explanation:

Part A

First, we find the lowest common multiple of 9,15, and 18.

To do this, express each number as a product of its prime factors.

`\begin{gathered} 9=3*3 \\ 15=3*5 \\ 18=2*3*3 \end{gathered}`

Next, multiply all prime factors the greatest number of times they occur in either number.

`\text{LCM}=2*3*3*5=90`

The LCM of 9, 15, and 18 is 90.

Part B

To answer this part, divide the LCM by the respective numbers:

(i)

`(90)/(9)=10`

9 divides into LCM 10 times.

(ii)

`(90)/(15)=6`

15 divides into LCM 6 times.

(iii)

`(90)/(18)=5`

18 divides into LCM 5 times.