Correct Answer - Option 2 : 429
Concept
LCM: The Least common multiple or lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b.
Calculation
The Least number divisible by 10, 14 and 42 = LCM(10, 14, 42)
10 = 2 × 5
14 = 2 × 7
42 = 2 × 3 × 7
⇒ LCM(10, 114, 42) = 210
The least number divisible by 10, 14 and 42 which leaves remainder 9 in each case = (210 × p) + 9, where 'p' is a natural number
⇒ (210 × p) + 9 is completely divisible by 13
Putting values of p = 1, 2, 3... etc we get,
For p = 1
(210 × p) + 9 = 210(1) + 9 = 219, which is not divisible by 13
For p = 2
(210 × p) + 9 = 210(2) + 9 = 429, which is divisible by 13
∴ The least number which when divided by 10, 14 and 42 leaves remainder 9 in each case but completely divisible by 13 is 429.
