x is the smallest number of 5-digits which when divided by 10, 15, 24, 35 and 42, leaves a remainder 7 in each case. The sum of the digits of x is:

Explanation

Given: Smallest number of 5 digits which is divided by 10, 15, 24, 35 and 42, leaves a remainder 7 in each case. Solution: LCM of 10, 15, 24, 35, and 42 ⇒ 10 = 2 × 5 ⇒ 15 = 3 × 5 ⇒ 24 = 2 × 2 × 2 × 3 ⇒ 35 = 5 × 7 ⇒ 42 = 2 × 3 × 7 LCM = 840 Smallest number of 5 digits = 10000 Smallest number of 5 digits which is divided by 840 = 840 × 12 = 10,080 Remainder 7 in each case = 10,080 + 7 = 10,087 Sum of digits (10,087) = 1 + 0 + 0 + 8 + 7 = 16 Sum of digits = 16