Question

The least number such that when divided by 15 25 35 and 45 it leaves remainder 7 17 27 and 37 respectively is

Answer 1

Answer:

Required Least Number is 1567.

Step-by-step explanation:

Answer:

Required Least Number is 1567.

Step-by-step explanation:

Given

Divisors are 15 , 25 , 35 and 45

Respective Remainders: 7 , 17 , 27 , 37

To find: Least Number divided by given divisors and leaves respective remainders.

15 - 7 = 8

25 - 17 = 8

35 - 27 = 8

45 - 37 = 8

Since, Difference between Divisors and remainders is 8 in each case.

So, we have to find LCM of the divisors and subtract 8 from them.

Using Prime factorization method,

15 = 3 × 5

25 = 5 × 5

35 = 5 × 7

45 = 3 × 3 × 5

LCM = 5 × 3 × 3 × 7 × 5 = 1575

Required Number = 1575 - 8 = 1567

Therefore, Required Least Number is 1567.

Answer 2

1567 as if we do the prime Facotree the answer is 1575-8 is 1567