What is the least number which when doubled will be exactly divisible by 12, 16, 22 and 26?

Question

What least number must be subtracted from 1739 so that the resulting number when divided by 6, 10 and 12 will leave in each case the same reminder 5?

Answer 1

3432

---

12 = 2*2*3
16 = 2*2*2*2
22 = 2*11
26 = 2*13
LCM (12,16,22,26) = 2*2*2*2*3*11*13 = 6864
6864/2=3432

Comments

1716 is also divisible by 12, 16, 22, and 26 when multiplied by 2
 and this number is smaller

---

are you sure? please double check