Question

the Gcf of two numbers is 3 and there lcm is 180 . if one of the numbers is 45 then the second number?​

Answer 1

To solve for the second number given the GCF and LCM of two numbers and one of the numbers, we can follow the steps below:

`\sf{Let\:the\:two\:numbers\:be\: represented\:by}`\:
`\sf{a\:and\:b,\:where\: a\: is \:given\: as\:45.`

\text{We know that the GCF of } a \text{ and } b \text{ is 3, which means that 3 is a factor of both } a \text{ and } b.} \

\text{We also know that the LCM of } a \text{ and } b \text{ is 180, which means that } a \text{ and } b \

\text{have no common factors other than 3, and their product divided by 3 equals 180:} \

a \times b &= 3 \times \text{LCM}(a, b) \

&= 3 \times 180 \

&= 540 \

\text{Since we know that } a = 45, \text{ we can substitute this into the equation above to solve for } b: \

45 \times b &= 540 \

\text{Dividing both sides by 45, we get:} \

b &= 12 \

\end{align*}

Therefore, the second number is 12.

Answer: b=12