Find the lowest number which is more by 6 to be divided by 25, 40 and 60 exactly
Answers
Answer:
609 is the answer
Step-by-step explanation:
we get the least value of (N – 9) = 600. Therefore, we get the least value of N = 609. Hence, 609 is the least number which when divided by 25, 40 and 60 leaves 9 as remainder in each case.
The lowest number which is more by 6 to be divided by 25, 40 and 60 exactly is 606.
Given: The numbers 25, 40, and 60.
To Find: The lowest number which divides 25, 40, and 60 exactly when decreased by 4.
Solution:
- We are required to find the lowest number, so we shall find the LCM of the given numbers.
- The LCM after being increased by a particular number gives us the lowest number which divides a set of numbers leaving a certain fixed remainder in each case.
Coming to the numerical, we have,
The numbers 125, 150, and 300.
We need to find the greatest number so we shall find the LCM first using the prime factorization method.
Writing the prime factors of the numbers, we get;
25 = 5 × 5
40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
∴ LCM ( 25, 40, 60 ) = 2 × 2 × 2 × 3 × 5 × 5
= 600
Now, it is said that the LCM must exactly divide the numbers when decreased by 6, so we shall increase the LCM by that number so that again after decreasing it, the original LCM comes.
So, the increased number is = 600 + 6
= 606
Hence, the lowest number which is more by 6 to be divided by 25, 40 and 60 exactly is 606.
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