Scholarship Exam Preparation App
Class 8 - (Math )
Operations on numbers - L.C.M., G.C.D
The product of two 2-digit numbers is 2400 and their LCM is 6 times their HCF. What is the difference between these two numbers?
a :
20
b :
40
c :
60
d :
10
Explanation :
Formula: Product of two numbers = HCF * LCM 2400 = HCF * (6 * HCF) 2400 = 6 * (HCF)² (HCF)² = 2400 / 6 = 400 HCF = 20
Since HCF = 20, LCM = 6 * 20 = 120.
Product of uncommon factors = LCM / HCF = 120 / 20 = 6.
Coprime factor pairs for 6 are (2, 3).
Find the numbers by multiplying factors with HCF:
First number = 2 * 20 = 40
Second number = 3 * 20 = 60 Both 40 and 60 are 2-digit numbers, which fits the condition.
Difference between the numbers = 60 - 40 = 20. Wait, let's recheck the options layout. Difference is 20, option b. Let's fix the choice marker. = 20
Since HCF = 20, LCM = 6 * 20 = 120.
Product of uncommon factors = LCM / HCF = 120 / 20 = 6.
Coprime factor pairs for 6 are (2, 3).
Find the numbers by multiplying factors with HCF:
First number = 2 * 20 = 40
Second number = 3 * 20 = 60 Both 40 and 60 are 2-digit numbers, which fits the condition.
Difference between the numbers = 60 - 40 = 20. Wait, let's recheck the options layout. Difference is 20, option b. Let's fix the choice marker. = 20