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Find the least number which when divided by 12, 15, 18 and 27 leaves remainders 10, 13, 16 and 25 respectively.
- A540
- B538
- C542
- D552
Answer not set
Discussion 1
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CCommunity
As per the given data,
LCM of 12, 15, 18 and 27 = 2 × 2 × 3 × 3 × 3 × 5 × 1 = 540
We need the remainders 10, 13, 16 and 25
⇒ 12 - 10 = 2, 15 - 13 = 2, 18 - 16 = 2, 27 - 25 = 2
∴ Difference is 2 in each case
⇒ We need to subtract 2 to from the LCM of 12, 15, 18, 27 = 540 - 2 = 538
∴ Least number = 538
LCM of 12, 15, 18 and 27 = 2 × 2 × 3 × 3 × 3 × 5 × 1 = 540
We need the remainders 10, 13, 16 and 25
⇒ 12 - 10 = 2, 15 - 13 = 2, 18 - 16 = 2, 27 - 25 = 2
∴ Difference is 2 in each case
⇒ We need to subtract 2 to from the LCM of 12, 15, 18, 27 = 540 - 2 = 538
∴ Least number = 538