How to find the least common denominator

A common denominator lets two fractions be measured in the same size of piece. Any common multiple works, but the least one keeps the numbers small, and small numbers mean fewer slips when your child adds or compares later.

The page teaches the prime-factor route instead of listing multiples. Each denominator is broken into primes, the primes are circled, and the LCD takes each prime as many times as it appears in the denominator that holds the most of it. Item b brings a quiet surprise: 24 and 7 share nothing, so their LCD, 168, is simply their product.

This is 6.NS.B.4, least common multiples, here stretched past the standard's limit of 12, put to work as in 5.NF.A.1.

Turn to item e, with 8/9, 2/12, and 11/24. The trap is to multiply two denominators and stop: 9 × 24 gives 216, and 216 sits right there among the boxes. "Is 216 the smallest number all three go into?"

Let your child write 9, 12, and 24 as primes before ticking anything. "Which prime shows up most in one number?" Three 2s from 24 and two 3s from 9 build 72.

Item d hides a different shortcut, since 24/4 is the whole number 6 and only 20 really matters.

A note for parents: the three tick-the-box questions are numbered 1, 3, 3 on page 1 and d, e, f on page 2. In c, the solution writes 2/3 where the problem shows 3/2; the LCD, 60, is still right.

The grocery store hands you a least common multiple at the checkout. Hot dogs often come 10 to a pack and buns 8 to a bag. Have your child work out how many of each to buy so nothing is left over, then confirm with primes: 2 × 5 and 2 × 2 × 2 make 40.

On a calendar, mark one chore every 4 days and another every 6 days, and find the first day both land together.

Before the next session, deal a few cards from the 24 Game and let your child break 24 into primes the way item b does.

When item e comes out as 72 and not 216, say what happened: "You looked for the smallest, not the first." Comparing fractions with like and unlike denominators is next.