Two numbers are in the ratio of 5:7 and their LCM is 385. Find the numbers.
- A54,77
- B54,76
- C55,77
- D55,76
Solution & Step-by-step Explanation
Let the two numbers be 5x and 7x, where x represents their highest common factor (HCF).
The Least Common Multiple (LCM) of 5x and 7x is given by:
LCM=5×7×x=35x
Given that the LCM is 385:
35x=385
x=
35
385
=11
Now substitute the value of x back to find the numbers:
First number=5x=5×11=55
Second number=7x=7×11=77
The numbers are 55 and 77.
The Least Common Multiple (LCM) of 5x and 7x is given by:
LCM=5×7×x=35x
Given that the LCM is 385:
35x=385
x=
35
385
=11
Now substitute the value of x back to find the numbers:
First number=5x=5×11=55
Second number=7x=7×11=77
The numbers are 55 and 77.