Maths Practice 3- Factors and Multiples -ITO

Factors and Multiples - Level 3

1. The HCF of two numbers is 17 and their LCM is 102. If one number is 34, the other is:

51 68 85 102

2. What is the least number that leaves remainder 1 when divided by 2, 3, 4, 5, and 6?

61 121 181 241

3. A number is divisible by both 12 and 18. The smallest such number is:

36 72 144 216

4. The sum of two numbers is 112 and their HCF is 14. How many such pairs exist?

2 3 4 5

5. Which of the following is a factor of both 2⁴ × 3² × 5 and 2³ × 3 × 5²?

2³ × 3 × 5 2² × 3 × 5 2³ × 3² × 5 2⁴ × 3 × 5

6. If the product of two numbers is 3780 and their HCF is 18, then their LCM is:

180 210 210 210

7. The greatest 4-digit number divisible by 12, 15, and 18 is:

9720 9828 9990 9996

8. The smallest number which when divided by 35 and 56 leaves the same remainder is:

280 420 560 840

9. Find the largest 3-digit number divisible by 8, 12, and 15.

960 972 984 996

10. If a number is divisible by both 8 and 9, the smallest such number is:

36 72 144 288

Solutions

1. 85 (Using HCF × LCM = Product of numbers → 17 × 102 = 34 × other)
2. 61 (LCM of 2–6 = 60, add 1 → 61)
3. 36 (LCM of 12 and 18 = 36)
4. 4 pairs possible
5. 2² × 3 × 5 = 60
6. LCM = 3780 ÷ 18 = 210
7. LCM(12,15,18) = 180 → Largest 4-digit multiple = 9990
8. LCM(35,56) = 280
9. LCM(8,12,15) = 120 → Largest 3-digit multiple = 960
10. LCM(8,9) = 72