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The least number which when divided by 15 leaves a remainder of 5, when divided by 25, leaves a remainder of 15 and when divided by 35 leaves a remainder of 25 is

The least number which when divided by 15 leaves a remainder of 5, when divided by 25, leaves a remainder of 15 and when divided by 35 leaves a remainder of 25 is Correct Answer 515

Given:

The given number = 15, 25, and 35

Remainders = 5, 15, 25 respectively 

Concept used:

LCM: Product of the greatest power of each prime factor, involved in the numbers.

HCF: Product of the smallest power of each common prime factor in the numbers.

The least number which when divided by a, b, c leaves remainder x, y, z respectively in each case such that

(a – x) = (b – y) = (c – z) = k

Number = lcm of (a, b, c) – k

Calculation:

15 = 3 × 5

25 = 5 × 5

35 = 5 × 7

LCM (45, 25, 35) = 3 × 52 × 7 = 525

Since the difference between divisor and remainder is 10.

Thus, least number = 525 - 10 = 515

Hence, the least number is 515.

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