Question

7. Which of the following is the LCM of 24, 48, and 80? A. 220 C. 260 B. 240 D. 280

8. What are the first 3 common multiples of 3, 4, and 6? A. 12, 24, 30 C. 12, 24, 36 B. 12, 24, 32 D. 12, 24, 42

9. Which of these multiples is the LCM of 12, 16, and 24? A. 24 C. 54 B. 48 D. 60

10.Alfred Jun visits the library once every 2 days. Jayson visits it once every 3 days while Justine Louie once every 4 days. They all meet one day in the library. After how many days will they meet in the library again? A. 12 C. 20 B. 16 D. 24​

Answer 1

7. 240

8. 12, 24, and 36

9. 48

10. 12

Explanation:

7. Do the multiple of 24, 48, and 80. Then find the LEAST common number that all three numbers have in common. (Answer: 240)

8. Do the multiple of 3, 4, and 6. Then find 3 LEAST common numbers that all three numbers have in common. (Answer: 12, 24, and 36)

9. Do the multiple of 12, 16, and 24. Then find the LEAST common number that all three numbers have in common. (Answer: 48)

10. Do the multiple of 2, 3, and 4. Then find the LEAST common number that all three numbers have in common. (Answer: 12)

STEPS ON HOW TO SOLVE:

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 3, 4, and 6. Write this prime number(2) on the left of the given numbers(3, 4, and 6), separated as per the ladder arrangement.

Step 2: If any of the given numbers (3, 4, 6) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.

Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 3, 4, and 6 is the product of all prime numbers on the left, i.e. LCM (3, 4, 6) by division method = 2 × 2 × 3 = 12.

Answer 2

`▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ { \huge \mathfrak{Answer}}▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪`

7.) LCM of 24, 48, 80

• 24 = 2 × 2 × 2 × 3

• 48 = 2× 2 × 2 × 2 × 3

• 80 = 2 × 2× 2 × 2 × 5

so, LCM = 2 × 2 × 2 × 2 × 3 × 5 = 240

8.) first three Common multiples of 3, 4, and 6

LCM = 12

first three common multiples of given numbers is first three multiples of their LCM, that is

• 12

• 24

• 36

9. LCM of 12, 16 and 24

• 12 = 2 × 2 × 3

• 16 = 2 × 2 × 2 × 2

• 24 = 2 × 2 × 2 × 3

LCM = 2 × 2 × 2 ×2 × 3 = 48

10. The day when the three of them will meet is LCM of the number of days they visit the library every week.

that is LCM of 2 , 3 and 4

that is 12