Question

smallest number which when divide by 25,40,60 leaves remainder 7 in each case

Answer 1

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Answer 2

Given: Three numbers 25, 40 and 60

To find: The smallest number which when divided by the given numbers, leaves remainder 7 in each case

Solution: To get the required number, first we need to calculate the smallest number which is exactly divisible by given numbers i.e., LCM.

Using prime factorization method:

25 = 5 × 5

40 = 2 × 2 ×  2 × 5

60 = 2 × 2 × 3 × 5

LCM is the product of maximum frequencies of all the factors of given numbers.

LCM = 2 × 2 × 2 × 3 × 5 × 5 = 600

The required number will be 7 more than the LCM i.e., 600 + 7 = 607.

Hence, the smallest number which when divided by 25, 40 and 60 leaves remainder 7 in each case is 607.