The GCF of 114 and x is 38; the LCM of 114 and x is 228. Find x .
A) x = 71
B) x = 152
C) x = 722
D) x = 76
E) x = 80

Question

The GCF of 114 and x is 38; the LCM of 114 and x is 228. Find x . ​
A) x = 71
B) x = 152
C) x = 722
D) x = 76
E) x = 80

Quizplus · Accepted Answer

The GCF (Greatest Common Factor) of 114 and x is 38, which means 38 is the highest number that divides both 114 and x without leaving a remainder. Since 114 is divisible by 38, we can find that 114 = 38 * 3. For the LCM (Least Common Multiple) of 114 and x to be 228 and the GCF to be 38, x must be a number that when multiplied by 114 through their lowest common multiple gives 228, and when divided by their greatest common factor gives 38. The LCM of two numbers a and b is given by (a*b)/GCF(a,b). Here, we know the LCM (228), and we know the GCF (38), so we can solve for x in the equation (114*x)/38 = 228. Simplifying this gives x = 76.

The GCF of 114 and X Is 38; the LCM