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<!DOCTYPE html>
<html data-require="math">
<head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
    <title>Least common multiple</title>
    <script src="../khan-exercise.js"></script>
</head>
<body>
    <div class="exercise">
        <div class="vars">
            <var id="C">randRange( 2, 6 )</var>
            <var id="START_A">randRange( 1, 10 )</var>
            <var id="START_B">randRangeExclude( 1, 10, [ START_A ] )</var>
            <var id="A">START_A * C</var>
            <var id="B">START_B * C</var>
            <var id="BIGGER">Math.max( A, B )</var>
            <var id="SMALLER">Math.min( A, B )</var>
            <var id="PRODUCT">A * B</var>
            <var id="GCD">getGCD( A, B )</var>
            <var id="LCM">PRODUCT / GCD</var>
            <var id="MULTIPLES">getMultiples( BIGGER, LCM )</var>
        </div>

        <div class="problems">
            <div>
                <div class="question">
                    <p>What is the least common multiple of <var>A</var> and <var>B</var>?</p>
                    <p>Another way to say this is:</p>
                    <p><code>\lcm(<var>A</var>, <var>B</var>) = {?}</code></p>
                </div>
                <p class="solution" data-forms="integer"><var>LCM</var></p>
            </div>
        </div>

        <div class="hints">
            <p>The least common multiple is the smallest number that is a multiple of <var>A</var> and <var>B</var>.</p>
            <p>We know that <var>A</var> x <var>B</var> (or <var>PRODUCT</var>) is a common multiple,
                but is it the least common multiple?</p>
            <p>Write out the multiples of <var>BIGGER</var> until we find a number divisible by <var>SMALLER</var>.</p>
            <span data-each="MULTIPLES as M"> <var>M</var>, </span>
            <p>So, <var>LCM</var> is the least common multiple of <var>A</var> and <var>B</var>.</p>
        </div>
    </div>
</body>
</html>
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