Common multiples and Common factors：練習問題

Which of the following numbers is a common multiple of \(6\) and \(8\)?

Two positive whole numbers, A and B, have a Highest Common Factor (H.C.F.) of \(8\) and a Least Common Multiple (L.C.M.) of \(144\).

If number \(A\) must be greater than \(10\) but less than \(60\), what is the value of the sum \(A + B\)?

The product of two numbers is $$720$$. If their Least Common Multiple (LCM) is $$180$$, what is their Highest Common Factor (HCF)?

Which of the following numbers is a common multiple of \(9\) and \(12\)?

First, find the Highest Common Factor (\(\text{H.C.F.}\)) of \(48\) and \(60\). Let this factor be \(F\).

Next, find the second smallest positive whole number that is a common multiple of \(F\) and \(18\).

Find the first two common multiples of \(9\) and \(12\).

Find the smallest common multiple of \(12\) and \(16\) that is greater than \(100\).

Let \(H\) be the Highest Common Factor (\(\text{H.C.F.}\)) of the numbers 56, 84, and 140. Let \(M\) be the Least Common Multiple (\(\text{L.C.M.}\)) of the numbers 12, 15, and 18.

Find the value of the smallest positive whole number that is a common multiple of \(H\) and \(M\). What is the sum of the digits of this resulting number?

A florist is making bouquets. There are 20 lilies and 28 roses. The florist wants to group the flowers so that each bouquet has the same number of lilies and the same number of roses, with no flowers left over.

Part a: List all the possible numbers of bouquets the florist can make by finding all the common factors of \(20\) and \(28\).

Part b: What is the Highest Common Factor (H.C.F.) of \(20\) and \(28\)?

Part c: Two flashing lights are turned on at the same time. Light A flashes every \(8\) seconds and Light B flashes every \(10\) seconds. After how many seconds will both lights next flash at the same time? (Find the Least Common Multiple (L.C.M.) of \(8\) and \(10\)).

A local bakery is managing production logistics involving common multiples and common factors for their goods.

Croissants are baked in batches of 15, and Muffins are baked in batches of 20. If the baker wants to produce the exact same total number of croissants and muffins, what is the smallest total number of croissants produced?

Let this minimum number be L.

The baker has 90 Scones and 120 Brownies. She wants to divide all of them into the greatest possible number of identical display boxes, such that every box contains the same number of scones and the same number of brownies, with no leftovers. What is the greatest number of identical display boxes she can prepare?

Let this maximum number be H.

Find the second smallest positive common multiple of L (the number from Part A) and H (the number from Part B).