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GCF and LCM Transitional Reasoning Practice

Math · Number Sense & Operations · Math · Counting & Place Value

2 Math practice questions on GCF and LCM. Questions that build towards applied reasoning.

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Questions

  1. 1.

    Two automated shuttle lines depart simultaneously from a logistics center; Line A has service checkpoints every 18 km, and Line B has service checkpoints every 24 km. The two lines share a joint maintenance hub at the shortest non-zero distance where checkpoints for both lines coincide. At this hub, workers distribute 75 digital gauges and 105 transmitters equally among the maximum possible number of identical repair kits without leaving any components behind. What is the sum of the distance from the logistics center to the maintenance hub (in kilometers) and the total number of items in a single repair kit?

    • A) 84
    • B) 87
    • C) 96
    • D) 156
  2. 2.

    A carpenter has two wooden beams with lengths of 84 cm and 140 cm. She cuts both beams into smaller planks of equal whole-number length without any leftover wood, making each plank as long as possible. Next, she lays several of these cut planks end-to-end in a straight line alongside prefabricated metal strips that are each 48 cm long. What is the minimum number of wooden planks needed so that their total combined length exactly matches a whole number of these metal strips?

    • A) 4
    • B) 6
    • C) 7
    • D) 12

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