GCF and LCM Transitional Reasoning Download PDF
5 Math practice questions on GCF and LCM. Questions that build towards applied reasoning.
Questions
- 1.
An urban planning team is installing streetlights along a straight avenue whose length is between 700 meters and 800 meters. Type A lights are placed along the north curb every 24 meters, and Type B lights are placed along the south curb every 30 meters, with both sides having a light at the very beginning and at the very end of the avenue. Reflective markers will be installed along the central dividing line at equal distances using the greatest possible whole-meter spacing that evenly divides both light intervals, starting at the beginning and continuing to the end. How many reflective markers in total will be placed along the central dividing line of the avenue?
- 2.
A carpentry workshop needs to cut two timber beams measuring 240 cm and 336 cm into smaller pieces of equal length with no leftover wood. To minimize the amount of cutting, every piece must be of the greatest possible length. If each cut is made across a single beam without stacking them, what is the minimum total number of cuts required to divide both beams?
- 3.
A botanical garden receives a shipment of rare tulip bulbs to be sorted into display trays. When the bulbs are arranged into trays of 14, 21, or 28 bulbs each, there are always 6 bulbs left over. If the total number of bulbs in the shipment is between 450 and 550, how many tulip bulbs are in the shipment?
- 4.
A municipal greenhouse has two rectangular seedbed sections: Section 1 measures 84 meters by 126 meters, and Section 2 measures 105 meters by 126 meters. The greenhouse manager wants to partition both sections entirely into congruent square planting plots of the largest possible area, with no ground left unused. If a drip irrigation emitter must be installed at the center of each square plot, what is the total number of emitters needed for both sections?
- 5.
Two autonomous transport shuttles, A and B, operate on separate closed tracks at a distribution center, completing one full circuit in 18 minutes and 30 minutes, respectively. Both shuttles depart simultaneously from the central depot, with Shuttle A loading 24 packages per circuit and Shuttle B loading 32 packages per circuit. At the exact moment both shuttles first return to the central depot at the same time, all loaded packages are sorted into identical delivery containers with equal numbers of Shuttle A packages and equal numbers of Shuttle B packages and none left over. If the maximum possible number of identical containers is prepared, how many total packages does each container hold?