Question

The least common multiple of two numbers is 36. The difference of the two numbers is 3. What are the numbers? Enter your answers in the boxes.

Answer 1

9 and 12

Step-by-step explanation:

It is given that the least common multiple of two numbers is 36 and the difference of the two numbers is 3.

We need to find both numbers.

The positive factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

List all the pairs (a,b), such that LCM(a,b)=36. The list of pairs and the difference of a and b is shown below.

Pair Difference

(1, 36) 36-1=35

(2, 36) 36-2=34

(3, 36) 36-3=33

(4, 36) 36-4=32

(6, 36) 36-6=30

(9, 36) 36-9=27

(12, 36) 36-12=24

(18, 36) 36-18=18

(36, 36) 36-36=0

(4,9) 9-4=5

(4, 18) 18-4=14

(9,12) 12-9=3 (Only this is true)

(12,18) 18-12=6

Since the difference of 9 and 12 is 3 and their LCM is 36, therefore, the two number are 9 and 12.

Answer 2

The numbers are 12 and 9.

Explanation:

Since, the factors of 36 are { 1, 2, 3, 4, 6, 9, 12, 18, 36 },

So, the pairs that having the LCM ( least common factor) of 36 are,

{ (1, 36), (2, 36), (3, 36), (4, 36), (6, 36), (9, 36), (12, 36), (18, 36), (4,9), (4, 18), (9,12), (12,18) }

Hence, the pair that having the difference of 3 is (9,12),

Therefore, the numbers that having LCM of 36 and difference of 3 are 12 and 9.