The LCM of two numbers is 60 and their HCF is 4. If one number is 20, find the other.
Explanation:
Using HCF × LCM = Product of numbers: 4 × 60 = 20 × other.
Therefore, other = 240 ÷ 20 = 12.
The HCF of two numbers is 12 and their LCM is 72. If one number is 24, find the other number.
Explanation:
Using HCF × LCM = Product of numbers: 12 × 72 = 24 × other number. 864 = 24 × other number.
Other number = 864 ÷ 24 = 36.
The LCM of two numbers is 144 and their HCF is 12. If one number is 36, what is the other?
Explanation:
HCF × LCM = Product of numbers. 12 × 144 = 36 × other. 1728 = 36 × other.
Other = 1728 ÷ 36 = 48.
Find the greatest number that can divide 150 and 200 with no remainder.
Explanation:
150 = 2 × 3 × 5², 200 = 2³ × 5².
Common factors: 2 and 5². HCF = 2 × 5² = 2 × 25 = 50.
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.
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.
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.
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.
