Question

24. A three-digit number 4BC is divisible by 15. What are the values of B and C for the
smallest such number.
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Answer 1

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Prime factorisation of 22=2×11
Prime factorisation of 33=3×11
Prime factorisation of 55=5×11
So, LCM 22,33,55=2×3×5×11=330
As 330 is the smallest 3− digit number divisible by 22,33,55, the number 330+5=335 will give a remainder 5 when divided by these numbers.
The highest 3− digit number is 999.
999 when divived by 330 gives a remainder 9, so 999−9=990 is the largest 3− digit number divisible by 22,33,55, the number 990+5=995 will give a remainder 5 when divided by these numbers.

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