If the LCM of two numbers is 60, and the difference between the two numbers is 3, what is the pair of numbers?!?!?!?
12 and 15
To find the pair of numbers, let's break down the problem step by step:
Step 1: Understand the problem.
The least common multiple (LCM) of two numbers is the smallest positive integer that is divisible by both numbers without leaving any remainder. In this case, the LCM is given as 60, and the difference between the two numbers is 3.
Step 2: Set up equations.
Let's assume the two numbers are x and y.
Based on the given information, we can set up two equations:
1) LCM(x, y) = 60
2) y - x = 3
Step 3: Solve the equations.
Using the first equation, we need to factorize 60 into the product of its prime factors. The prime factorization of 60 is 2 x 2 x 3 x 5.
To find the values of x and y, let's start by assigning possible values to each prime factor, keeping in mind that the difference between the two numbers is 3.
One possible combination is:
x = 2 x 3 = 6
y = 2 x 2 x 5 = 20
In this case, the difference between the two numbers (y - x) is indeed 3.
So, the pair of numbers that satisfies the given conditions is 6 and 20.