What is the largest four-digit number that is exactly divisible by 12, 15 and 20?

9,960Correct answerYour answer9,980Correct answerYour answer9,990Correct answerYour answer9,996Correct answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

A number divisible by 12, 15 and 20 is a multiple of $\operatorname{LCM}(12, 15, 20) = 60$ .
$9999 \div 60 = 166$ , remainder 39.
Largest multiple = $9999 - 39 = 9{,}960$ .

Worth noting

9,980 is divisible by 20 only, 9,990 by 15 only, and 9,996 by 12 only. The number must be a multiple of all three, that is, of the LCM 60.

Ten questions from HCF & LCM, at your own pace.

Explanation