Using the relationship between HCF, LCM, and product: HCF * LCM = Product. Thus, LCM = 100 / 5 = 20.

Using the relation HCF * LCM = Product of the numbers, we have LCM = 1000 / 5 = 200.

The numbers can be 16 and 24, as their HCF is 8 and LCM is 48.

Using the relationship between HCF, LCM, and the product of two numbers: LCM = Product / HCF = 288 / 8 = 36.

The maximum product occurs when the numbers are 2, 10, and 6, giving a product of 120.

The maximum product of the three numbers can be calculated as (LCM * HCF^2) = 180 * 3^2 = 5400.

The product of the three numbers is equal to LCM * HCF^2. Therefore, 180 * 3^2 = 180 * 9 = 1620.

The product of two numbers is equal to the product of their LCM and HCF. Therefore, 120 * 10 = 1200.

The product of two numbers is equal to the product of their LCM and HCF. Therefore, 120 * 5 = 600.

Let the two numbers be 15a and 15b. Then, LCM = 15ab = 180, so ab = 12. The pairs (3, 4) give the numbers 45 and 60, summing to 105.

Using the relation LCM(a, b) = (a * b) / HCF(a, b), we can find the other number. Here, 60 = (15 * x) / HCF(15, x). The other number is 60 / 15 = 4.

The product of two numbers is equal to the product of their LCM and HCF. Therefore, 60 * 4 = 240.

Let the two numbers be 5a and 5b. Then, LCM(5a, 5b) = 5 * LCM(a, b) = 60, which gives LCM(a, b) = 12. The pairs (3, 4) work, giving numbers 15 and 20, which sum to 35.

Using the relationship between LCM and the numbers: (24 * x) / HCF = 72. The other number is 36.

Let the other number be x. Then, 84 = (21 * x) / 7. Solving gives x = 28. The sum is 21 + 28 = 49.

The HCF of 18 and 24 is 6, as it is the largest number that divides both.

Let the numbers be 2x and 3x. Then, LCM(2x, 3x) = 6x = 60, which gives x = 10. The numbers are 20 and 30, and their sum is 50.

Initially, there are 36 boys and 24 girls. After the changes, there will be 46 boys and 19 girls. The new ratio is 46:19, which simplifies to approximately 4:3.

Initially, there are 36 boys and 24 girls. After increasing boys by 5, there will be 41 boys and 24 girls, giving a new ratio of 41:24, which simplifies to approximately 4:3.

Initially, there are 36 boys and 24 girls. After increasing the boys by 10, there will be 46 boys and 24 girls, giving a new ratio of 46:24, which simplifies to 4:3.

Let the number of boys be 3x and girls be 2x. Then, 3x + 2x = 50, which gives x = 10. Therefore, boys = 3x = 30.

Let the ages be 4x and 5x. Then, 4x + 5x = 72, leading to 9x = 72, so x = 8. The older sibling's age is 5x = 40.

The pair 5 and 12 has an HCF of 1 and an LCM of 60.

Using the relation HCF * LCM = Product of the numbers, we have 7 * 84 = 21 * x, which gives x = 42.

Using the relation HCF * LCM = Product of the numbers, we have 8 * 120 = 32 * x, which gives x = 40.

Using the relation: LCM * HCF = Product of the numbers, we have 84 * 12 = 36 * x, solving gives x = 28.

Let the two numbers be 12x and 12y. Then, LCM(12x, 12y) = 12 * LCM(x, y) = 84, which gives LCM(x, y) = 7. The pairs (x, y) that satisfy this are (3, 4) or (4, 3), leading to 24 and 42.

Let the two numbers be 12a and 12b. Then, 12ab = 84, so ab = 7. The pairs (1, 7) and (7, 1) give us 12 and 84, which sum to 96.

The LCM of 15 and 20 is 60 seconds. Therefore, they will toll together again at 12:01 PM.

Using the relationship between HCF, LCM, and the numbers: (21 * x) / 7 = 84. Solving gives x = 42.