Showing 31–40 of 151 questions
in HCF and LCM
If HCF of two numbers is 15 and their product is 2700, find their LCM.
Explanation:
Using the formula: HCF × LCM = Product of two numbers. 15 × LCM = 2700, so LCM = 2700 ÷ 15 = 180.
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.
Find the HCF of 45, 60, and 75.
Explanation:
45 = 3² × 5, 60 = 2² × 3 × 5, 75 = 3 × 5².
Common factors: 3 and 5. HCF = 3 × 5 = 15.
What is the LCM of 20, 30, and 40?
Explanation:
20 = 2² × 5, 30 = 2 × 3 × 5, 40 = 2³ × 5. LCM = 2³ × 3 × 5 = 8 × 3 × 5 = 120.
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.
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.
