High School

The HCF of 182 and X is 26, and the LCM of 182 and X is 1092. Determine the value of X.

A) 364
B) 156
C) 78
D) 91

Answer :

Final answer:

The value of X that satisfies the given conditions, where the HCF of 182 and X is 26, and the LCM is 1092, is 156 after applying the formula HCF times LCM = 182 times X, hence the answer is b. 156

Explanation:

The question involves finding the value of X when the Highest Common Factor (HCF) of 182 and X is 26, and the Lowest Common Multiple (LCM) of 182 and X is 1092.

We know that the product of the HCF and LCM of two numbers is equal to the product of the numbers themselves. Therefore, we can use the formula

HCF times LCM = 182 times X. Plugging in the values we have,

26 times 1092 = 182 times X. Simplifying this gives us

28392 = 182X, and solving for X, we get X = 28392/182, which simplifies to X = 156.

Thus, the value of X that satisfies the given conditions is 156.