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)?
A6.5 minutes
B7.2 minutes
C36 minutes
DCannot be determined
Correct Answer:
B. 7.2 minutesExplanation:
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.
A24 and 40
B16 and 32
C18 and 30
D12 and 20
Correct Answer:
A. 24 and 40Explanation:
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.
