Multiple choice

What is the least possible number which when divided by 12 , 15, 20 and 54 leaves remainder 4 ?

  1. 544

  2. 644

  3. 444

  4. 378
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A Correct answer
Explanation

Find LCM of 12, 15, 20, 54. Prime factors: 12=2²×3, 15=3×5, 20=2²×5, 54=2×3³. LCM = 2²×3³×5 = 540. The number must be 540k + 4. Smallest such number is 540 + 4 = 544. Verify: 544 ÷ 12 = 45R4, 544 ÷ 15 = 36R4, 544 ÷ 20 = 27R4, 544 ÷ 54 = 10R4.

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