The least common multiple of two numbers is 60 and one of the numbers is seven less than the other. What are the two numbers? HEEEEEEEEEEEEELLLLLLLLLLLLPPPPPPP!!!!!!

multiples of 60:

2, 30,
3, 20,
4, 15,
5, 12,
6, 10

Can someone help me with my questions please. HELP!

No

To find the two numbers, let's break down the problem step by step.

First, let's assign variables to the two numbers. Let's call the first number "x" and the second number "y."

We are given that the least common multiple (LCM) of the two numbers is 60. The LCM is the smallest number that both x and y divide evenly into. Therefore, we can write:

LCM(x, y) = 60

Next, we are given that "one of the numbers is seven less than the other." This can be expressed as:

x = y - 7

Now, let's use these two equations to solve for x and y simultaneously.

Substitute the value of x from the second equation into the first equation:

LCM(y - 7, y) = 60

Now, we need to find the least common multiple of y - 7 and y. To do this, we need to factorize both numbers.

The prime factorization of y - 7 can be written as (y - 7) = p₁^a₁ * p₂^a₂ * ...

The prime factorization of y can be written as y = p₁^b₁ * p₂^b₂ * ...

The least common multiple will contain all the prime factors with their highest exponent. So, we take the highest exponent for each prime factor:

LCM(y - 7, y) = p₁^max(a₁, b₁) * p₂^max(a₂, b₂) * ...

Since we know that LCM(x, y) = 60, we can set up the equation:

p₁^max(a₁, b₁) * p₂^max(a₂, b₂) * ... = 60

From here, we need to find the prime factorization of 60 and set the exponents to the appropriate maximum values in the equation above. The prime factorization of 60 is:

60 = 2^2 * 3 * 5

To have an LCM of 60, we need to set the exponents in the equation above to:

max(a₁, b₁) = 2
max(a₂, b₂) = 1
max(a₃, b₃) = 1

Now, we can solve for y by substituting these values back into the prime factorization of y:

y = p₁^b₁ * p₂^b₂ * ...

Substituting the values for the exponents:
y = 2^2 * 3 * 1

This simplifies to:
y = 12

Finally, we can find x by substituting the value of y into the given equation x = y - 7:

x = 12 - 7
x = 5

Therefore, the two numbers are x = 5 and y = 12.