Question

1. Find the least 5-digit number which on dividing by 4, 12, 20 and 24 leaves a
remainder 3 in each case.






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Answer 1

Step-by-step explanation:

Least 5 digit number  = 10000.

LCM(4,12,20,24) = 120

Dividing 10000 by 120 leaves a remainder 40 , Subtract 40 from 10000 = 9960

So this means 9960 is divisible by 120.

9960 + 120 = 10080.

To find the number which leaves remainder 3, we have to add 3 to 10080.

10080 + 3 = 10083.

Hope this helps!

Answer 2

Answer:

Least number when divided by 12,16,24,36 and leaves remainder 0

=LCM of 12,16,24,36

So,LCM leaves remainder 0

So,Required number will be 7 more than LCM

∴ Required number=LCM+7

Factors of 12=2×3×2

Factors of 16=2×2×2×2

Factors of 24=2×2×2×3

Factors of 36=2×2×3×3

∴ LCM=2×2×2×2×3×3=16×9=144

So,Required number=LCM+7=144+7=151

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