Greatest Common Factor (GCF) / Least Common Multiple (LCM)：練習問題

A school choir has 24 boys and 36 girls. The teacher wants to divide them into several groups such that each group has the same number of boys and the same number of girls. What is the greatest number of groups that can be formed?

A rectangular floor measures \(120\text{ cm}\) by \(168\text{ cm}\). If the floor is to be completely covered by identical square tiles without any overlapping or gaps, what is the length of the side of the largest possible square tile?

Three neon signs flash at different intervals. The first sign flashes every \(48\) seconds, the second flashes every \(72\) seconds, and the third flashes every \(108\) seconds. If they all flash together at \(8:00\text{ p.m.}\), what is the next time all three signs will flash at the same moment?

Find the Greatest Common Factor (GCF) of 30, 45, and 75.

Find the difference between the Least Common Multiple (LCM) of 12 and 15 and the Greatest Common Factor (GCF) of 12 and 15.

Find the Least Common Multiple (LCM) of \(8\) and \(14\).

A bell rings every \(10\) minutes and another bell rings every \(15\) minutes. If they both ring at \(8:00\text{ a.m.}\), what is the next time they will ring together again?

A company produces gift boxes. One machine produces boxes in batches of 42, and another machine produces boxes in batches of 60.
(a) What is the smallest total number of boxes each machine must produce such that they have both produced the same number of boxes?
(b) If each box is a cube with a side length of 14 cm, and these boxes are packed into the smallest possible larger cubical crate without any gaps, what is the side length of that crate in cm?
(c) Using the side length found in (b), how many such boxes can fit into that crate?

A baker has 45 strawberry tarts and 60 blueberry tarts.
(a) He wants to pack them into boxes such that each box has the same number of strawberry tarts and the same number of blueberry tarts. What is the greatest number of boxes he can pack if all tarts must be used?
(b) Based on the answer in (a), how many tarts of each kind will be in one box?

A rectangular floor measures \(120\text{ cm}\) by \(160\text{ cm}\).
(a) Find the Greatest Common Factor (GCF) of 120 and 160.
(b) If the floor is to be covered completely by identical square tiles without any overlapping or gaps, what is the largest possible side length of each square tile?
(c) How many such square tiles are needed to cover the entire floor?