If the ratio of two numbers is 5 : 3 and the product of their LCM and their HCF is 135, then the sum of the reciprocals of the LCM and the HCF is:
Given:
The ratio of the two numbers is 5 : 3
The product of their LCM and HCF is 135
Formula Used:
LCM × HCF = Product of the numbers
Solution:
Let the two numbers be 5x and 3x
The product of the numbers:
(5x) × (3x) = 135
15x2 = 135
x2= = 9
x = 3
The two numbers are 5x = 15 and 3x = 9
The HCF of 15 and 9 is 3, and the LCM of 15 and 9 is 45
The sum of the reciprocals of the LCM and HCF:
=
Thus, the sum of the reciprocals of the LCM and HCF =
English
100 Questions
100 Marks
90 Mins English English100 Questions100 Marks90 Mins English English100 Questions100 Marks90 Mins EnglishFind the smallest number which, when divided by 12,18 and 24 , leaves a remainder of 5 in each case.
What is the largest 4 digit number that is divisible by 3,7,11,13 ?
The number of pairs of positive integers whose sum is 99 and HCF is 9 is
Find the HCF of 2.8, 11.2 and 0.84 .
Find the smallest number which when increased by 20 is completely divisible by 12, 20, 15, 18 and 24.
The LCM of the numbers 3.7 and 0.068 is:
Find the Highest Common Factor (HCF) of 372, 732 and 2196.
If the HCF of the expressions (x + 3) (2x² – 3x + a) and (x – 2) (3x² + 10x – b) is x² + x – 6, then what is the value of (2a – 3b) ?
The sum of two numbers is 1580 and their LCM is 18816. Find the two numbers.
Suggested Test Series
Suggested Test Series
Find the smallest number which, when divided by 12,18 and 24 , leaves a remainder of 5 in each case.
What is the largest 4 digit number that is divisible by 3,7,11,13 ?
The number of pairs of positive integers whose sum is 99 and HCF is 9 is
Find the HCF of 2.8, 11.2 and 0.84 .
Find the smallest number which when increased by 20 is completely divisible by 12, 20, 15, 18 and 24.
The LCM of the numbers 3.7 and 0.068 is:
Find the Highest Common Factor (HCF) of 372, 732 and 2196.
If the HCF of the expressions (x + 3) (2x² – 3x + a) and (x – 2) (3x² + 10x – b) is x² + x – 6, then what is the value of (2a – 3b) ?
The sum of two numbers is 1580 and their LCM is 18816. Find the two numbers.
