Question

Find the smallest positive integer value of n for which 225n is a multiple of 540

Answer 1

Well if u simplify 225n/540 u get 12n/5 it's much easier to figure out then and u get n=12

Answer 2

small typo
that should say 5n/12

Answer 3

Step 1: find the lowest common multiple of both the numbers.

Answer 4

$$\large 225 = 3^2 \cdot 5^2$$ and $$\large 540 = 2^2 \cdot 3^3 \cdot 5 $$If 225n is a multiple of 540,
then
$$\large 3^2 \cdot 5^2 \cdot n = 2^2 \cdot 3^3 \cdot 5 \cdot k$$
where k and n are integers (which can be written as products of primes).

What could n and k be to balance this equation?

Answer 5

Obviously, k = 5 on the RHS.

That leaves $$n = 2^2 \cdot 3 = 12$$