Question

Find the smallest value of n such that the LCM
of n and 15 is 45.
​

Answer 1

Answer:

plz mark me as brainlist

Step-by-step explanation:

The prime factors of 45 are 3, 3, 5. That means the two numbers for which the LCM is 45 have a combined set of prime factors - discarding duplicates - of 3, 3, 5.

The prime factors of 15 are 3, 5. That explains where the 5 and one of the 3’s came from in the LCM of 45.

What remains is what requires not one, but two 3’s. Fortunately, it’s not difficult to figure out. 3 x 3 = 9.

The other number that you’re looking for is 9.

1. 3x3x5 = 45 (LCM)
2. 3 x 5 = 15
3. 3x3 = 9 (n)

Answer 2

Smallest value of n such that the LCM of n and 15 is 45.

Step 1: Prime factorization of 45:

45 →9 * 5 →3 * 3 * 5

Step 2: LCM of 15 and 3 = 15

Step 3: LCM of 15 and 5 = 15

Step 4: LCM of 15 and 9 = 45