If the GCF (x, 36) is 4 and LCM (x, 36) is 288, then find the number x.
LCM(x,36) = x*36 / GCD(x,36)
so,
288 = 36x / 4
Murad
To find the number x, we can use the relationship between the greatest common factor (GCF) and the least common multiple (LCM) of two numbers.
The formula to find the LCM of two numbers, given their GCF, is:
LCM(x, 36) = (x * 36) / GCF(x, 36)
Given that the GCF(x, 36) is 4 and the LCM(x, 36) is 288, we can substitute these values into the formula:
288 = (x * 36) / 4
To solve for x, we can multiply both sides of the equation by the reciprocal of 36/4, which is 4/36:
288 * 4/36 = x
Simplifying the equation:
288 * 4 = 36x
1152 = 36x
Dividing both sides of the equation by 36:
1152 / 36 = x
Simplifying:
32 = x
Therefore, the number x is 32.
To find the number x, we need to understand the relationship between the greatest common factor (GCF) and the least common multiple (LCM) of two numbers.
The GCF of two numbers is the largest number that both numbers can be divided by without leaving a remainder. In this case, the GCF of x and 36 is 4. This means that both x and 36 are divisible by 4.
The LCM of two numbers is the smallest number that is a multiple of both numbers. In this case, the LCM of x and 36 is 288. This means that both x and 36 are factors of 288.
We know that the GCF of x and 36 is 4, so both x and 36 are divisible by 4. Additionally, we know that the LCM of x and 36 is 288, so both x and 36 are factors of 288.
To find x, we need to find the factors of 288 that are divisible by 4. Let's list the factors of 288: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, and 288.
Out of these factors, we need to find the one that satisfies both conditions: divisible by 4 and a factor of 288. The only factor that satisfies both conditions is 36.
Therefore, the number x is equal to 36.