LCM and HCF of two numbers are 114 and 19 respectively. If one of the numbers is 57, then find the other number.

Correct option is A

Given:

​The Least Common Multiple (LCM) of two numbers is 114.

The Highest Common Factor (HCF) of the two numbers is 19.

One of the numbers is 57.

Concept Used:

The relationship between the LCM, HCF, and the two numbers can be expressed as:

LCM × HCF = Number 1 × Number 2

Solution: 

Let the two numbers be A and B. From the problem, we know:

LCM = 114

HCF = 19

One of the numbers, say A=57, and we need to find the other number B

Using the formula: 

LCM × HCF = A × B

Substituting the known values:

114 × 19 = 57 × B 

2166 = 57 × B 

​$$B= \frac {2166}{57}$$ 

B = 38 

Thus the other number is $38$.​