Question

Find the least three digit number which when divided by 20, 30, 40 and 50 leaves remainder 10 in each case.

Answer 1

20 = 1 × 2 × 2 × 5 = 2² × 5¹
30 = 1 × 2 × 3 × 5 = 2¹ × 3¹ × 5¹
40 = 1 × 2 × 2 × 2 × 5 = 2³ × 5¹
50 = 1 × 2 × 5 × 5 = 2¹ × 5²
LCM of 20, 30, 40 and 50 = 2³ × 3¹ × 5² = 600
∴ Required number = 600 + 10 = 610.
Hence, the least three digit number which when divided by 20, 30, 40 and 50 leaves remainder 10 in each case is 610.