HCF and LCM
If the HCF of 408 and 468 is 36, find their LCM.
A
4728
B
5304
C
4680
D
5184
Explanation:
HCF × LCM = Product of numbers. 36 × LCM = 408 × 468. LCM = (408 × 468) ÷ 36 = 190944 ÷ 36 = 5304.
Three numbers are in ratio 2:3:4 with HCF = 5. What is their LCM?
A
1200
B
600
C
300
D
2400
Explanation:
Numbers are 10, 15, 20. 10 = 2 × 5, 15 = 3 × 5, 20 = 2² × 5. LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60 × 10 = 600.
Find the largest number that divides 247, 328, and 409 leaving remainder 7 in each case.
Explanation:
Required number divides (247-7), (328-7), (409-7) = 240, 321, 402. HCF(240, 321, 402) = 120.
The product of HCF and LCM of two numbers is 360. If one number is 20, find the other.
Explanation:
HCF × LCM = Product of numbers = 360. 360 = 20 × other number.
Other number = 360 ÷ 20 = 18.
Bell A rings every 12 minutes and Bell B rings every 18 minutes. After how many minutes will they ring together again if they ring at the same time now?
A
24 minutes
B
36 minutes
C
48 minutes
D
60 minutes
Correct Answer:
B. 36 minutes
Explanation:
They ring together after LCM(12, 18) minutes. 12 = 2² × 3, 18 = 2 × 3². LCM = 2² × 3² = 36 minutes.
Find HCF of 144, 180, and 192.
Explanation:
144 = 2⁴ × 3², 180 = 2² × 3² × 5, 192 = 2⁶ × 3.
Common factors: 2² and 3. HCF = 2² × 3 = 12.
The HCF of two numbers is 6. If their LCM is 60 and one number is 12, find the other number.
Explanation:
Using HCF × LCM = Product: 6 × 60 = 12 × other. 360 = 12 × other.
Other = 360 ÷ 12 = 30.
Four numbers are in the ratio 1:2:3:4 with HCF = 7. Find their LCM.
A
840
B
1680
C
420
D
2520
Explanation:
Numbers are 7, 14, 21, 28. 7 = 7, 14 = 2 × 7, 21 = 3 × 7, 28 = 2² × 7. LCM = 2² × 3 × 7 = 4 × 3 × 7 × 2 = 1680.
Two numbers have an HCF of 12. If one number is 60, find the other number such that their LCM is 180.
Explanation:
Using the formula: HCF × LCM = Product of two numbers
12 × 180 = 60 × Other number
2160 = 60 × Other number
Other number = 2160 ÷ 60 = 36
Verification: HCF(60, 36) = 12 ✓ and LCM(60, 36) = 180 ✓
The HCF of two numbers is 15 and their LCM is 450. If one of the numbers is 90, what is the other number?
Explanation:
Using HCF × LCM = Product of two numbers:
15 × 450 = 90 × Other number
6750 = 90 × Other number
Other number = 6750 ÷ 90 = 75
Verification: HCF(90, 75) = 15 ✓ and LCM(90, 75) = 450 ✓
