ASVAB Arithmetic Reasoning Practice: Finding the Least Common Denominator

By Consumer Dummies

Finding the least common denominator, or LCD, is useful to know for the Arithmetic Reasoning subtest on the ASVAB. Here are some practice questions that will prepare you for test day.

Practice questions

  1. Bonnie and Kathleen went shopping. Kathleen spent half her money on a beekeeping suit, one-third of her money on a ukulele, and one-tenth of her money to take Bonnie to lunch. If Kathleen came home with $12, how much money did she have to begin with?

    A. $175
    B. $177.50
    C. $180
    D. $182.50

  2. Sgt. 1st Class Stith has been asked to make his famous caramel sauce for his unit’s family fun day. However, when he was pouring the sugar, half of it spilled on the floor, a quarter of it spilled on the counter, and one-sixth of it spilled into the sink. Just three tablespoons remained in the container. How much sugar was originally in the container?

    A. 36 tablespoons
    B. 38 tablespoons
    C. 19 tablespoons
    D. None of the above

Answers and explanations

  1. The correct answer is Choice (C).

    Let x represent the amount of money Kathleen started with. Create an equation representing the sum of her purchases and the remaining money:

    ASVAB_2701

    The least common denominator for all those denominators is 30. Multiply each part of the equation by 30:

    ASVAB_2702

    Solve the equation normally to find x:

    ASVAB_2703

    Kathleen started out with $180.

  2. The correct answer is Choice (A).

    Remember that the whole is equal to the sum of the parts. Let x represent the original amount of sugar in Sgt. 1st Class Stith’s container and create an equation that accounts for every tablespoon of sugar like this:

    ASVAB_2704

    Get rid of all the fractions by finding the least common denominator. In this case, it’s 12, so multiply each term by 12 and cancel the denominators:

    ASVAB_2705

    Combine like terms and solve for x, which is the original amount of sugar in Sgt. 1st Class Stith’s container:

    ASVAB_2706

    There were originally 36 tablespoons of sugar in the container.