the LCM of two numbers is 51 times their H.C.F. If one number
is 27, find the other.
Answers
Answer: The other number cannot be determined using the given conditions since two unknown variables are there. Another condition is required for solving this problem.
Step-by-step explanation:
The relation between LCM and HCF if two numbers( a,b) can be given as:
LCM × HCF = a × b
Here, condition is given as:
LCM = 51 HCF
So, on substituting this value in the main formula we get:
51 HCF × HCF = 27 × b ( one of the numbers is given as 27)
Value of HCF and b( the second number) both are unknown and so it cannot be solved further without any other data.
Answer:
153
Step-by-step explanation:
We can list down the prime factors of 27.
The prime factors of 27 are as follows:
27 = 3 × 3 × 3
The prime factors of 51 are as follows:
51 = 3 × 17
The other number must be a multiple of 17 and 3 since 17 is also prime number.
The number should be however more than 51.
27 is divisible by : 3, 9 , 27
The lcm could therefore be :
51 × 3 = 153
51 × 9 = 459
51 × 27 = 1377
Since 153 is not divisible by 27 we eliminate it and take 459.
The HCF is 9 and the other number is 153 since 459 is divisible by 27 and 153.
The other number is thus 153 and the HCF is 9.