Two pipes fill a tank in 12 and 18 minutes respectively. After how many minutes will they both fill the tank together (in terms of LCM concept)?
A 6.5 minutes
B 7.2 minutes
C 36 minutes
D Cannot be determined
Correct Answer:
B. 7.2 minutes Explanation:
LCM(12, 18) = 36.
Time for both = 36/(36/12 + 36/18) = 36/(3 + 2) = 36/5 = 7.2 minutes.
What is the HCF of 72 and 90?
Explanation:
72 = 2³ × 3², 90 = 2 × 3² × 5.
Common factors: 2 and 3². HCF = 2 × 3² = 2 × 9 = 18.
The ratio of two numbers is 3:5 and their HCF is 8. Find the two numbers.
A 24 and 40
B 16 and 32
C 18 and 30
D 12 and 20
Correct Answer:
A. 24 and 40 Explanation:
Let numbers be 3k and 5k.
Their HCF is k = 8.
So numbers are 3(8) = 24 and 5(8) = 40.
Find the smallest number that is divisible by 12, 18, and 24.
Explanation:
12 = 2² × 3, 18 = 2 × 3², 24 = 2³ × 3. LCM = 2³ × 3² = 8 × 9 = 72.
If the HCF of 408 and 468 is 36, find their LCM.
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?
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.
