Find the greatest 3 digit number which when divided by 35,40 and 60 leaves the remainder 3 in each case
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The required number is "843".
Step-by-step explanation:
We know that, the greatest number of 3 digits is 999.
LCM of 35, 40, 60
35 = 5 × 7,
40 = 2 × 2 × 2 × 5 and
60 = 2 × 2 × 3 × 5
∴ LCM of 35, 40, 60 = 2 × 2 × 2 × 3 × 5 × 7 = 840
On dividing 999 by 840,
∴ 999 = 840 × 1 + 159
Remainder = 159
∴ The greatest three digits number which are divisible by 35, 40 and 60
= 999 - 159 = 480
Hence, the required number is (840 + 3) 843.
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