Common multiples in P4: list both, find the first match

Every spy needs gadgets. This one has a pair of swimming goggles strapped round his red beanie, a phone made of two paper cups on a string and a secret HQ under the dining table, draped in a blanket. "Goggles on. Not a sound." The Mastermind has a mission, "Operation Silent Owl", and a plan: "Five questions a day." The Partner, field agent for the day, in dark sunglasses with a juice box in hand, is not convinced. "...Five?"

That is Operation Silent Owl, the fifth episode of our comedy series, The Mastermind. Watch it first (it is under a minute), then read on. The code to the secret briefcase is a piece of Primary 4 math.

Operation Silent Owl: five questions a day, one hoot each.

The mission file is stamped CLASSIFIED: Whole Numbers, Fractions and Decimals. The signal is "one hoot", so every question card gets a flat, very audible "Hoot." from the Partner and an instant shush from the Mastermind. On the fifth hoot, a cardboard briefcase slides in. Its tag reads: "Code: the first common multiple of 4 and 6." Two narration boxes list the multiples calmly, "Multiples of 4: 4, 8, 12" and "Multiples of 6: 6, 12", and the two 12s are circled in red. "The code is 12." The briefcase clicks open on a practice notebook. The Partner sums it up flatly: "So the secret mission is... practice."

He has a point. And the method that cracks that lock is one your child can use for every common multiple in Primary 4.

What a common multiple is

A multiple of a number is what you get when you multiply it by 1, 2, 3 and so on. The multiples of 4 are 4, 8, 12, 16, 20 and on forever. Saying them out loud is just skip-counting in fours.

A common multiple of two numbers is a number that is on both lists. "Common" here means shared, like a common room. Finding the common multiples of two 1-digit numbers is part of Whole Numbers in Primary 4, alongside factors.

A few things trip children up:

Multiples and factors sound alike. Multiples of 4 start at 4 and keep growing. Factors of 12 (1, 2, 3, 4, 6 and 12) are never bigger than 12. A child who mixes the two words will list the wrong things.
There is no single answer. Two numbers have many common multiples. A question usually asks for the first one, or the first two or three.
The answer is not on show. You only find it by building the lists, so a careful method beats a guess.

The method: list both, find the first match

List the multiples of the first number. Skip-count, writing each one down.
List the multiples of the second number directly underneath.
Stop at the first number that appears in both lists. Circle it in both places, just as the episode does. That is the first common multiple.

Lining the two lists up, one under the other, makes the match easy to see.

Worked example 1: the briefcase code

Find the first common multiple of 4 and 6.

Step 1: List the multiples of 4. 4, 8, 12.

Step 2: List the multiples of 6. 6, 12.

Step 3: Find the first match. 4 and 8 are not on the list for 6, and 6 is not on the list for 4. The first number on both lists is 12. Circle both 12s.

Step 4: Check. 3 × 4 = 12 and 2 × 6 = 12, so 12 really is a multiple of both. The first common multiple of 4 and 6 is 12. The code is 12.

Worked example 2: the same day again

Here is the everyday version. One activity happens every 4 days and another happens every 6 days. Both happen today. When do they next fall on the same day?

Activity	Happens again after
Every 4 days	4 days, 8 days, 12 days
Every 6 days	6 days, 12 days

The first number on both lists is 12, so the two activities fall on the same day again after 12 days. Your child has just used a common multiple to answer a real question.

Worked example 3: a quicker way to list

Find the first common multiple of 6 and 8.

Instead of two long lists, list the multiples of the bigger number and check each one against the smaller number:

8: is it a multiple of 6? No.
16: is it a multiple of 6? No.
24: is it a multiple of 6? Yes, 4 × 6 = 24.

The first common multiple of 6 and 8 is 24. Check: 3 × 8 = 24. The bigger number's list reaches the match in fewer steps.

More than one common multiple

If a question asks for the first three common multiples of 4 and 6, keep both lists going. The matches are 12, 24 and 36. Notice the pattern: every common multiple of 4 and 6 is a multiple of 12. Once your child has found the first match, the next ones come quickly.

In Secondary 1, your child will meet the first common multiple again under a new name: the lowest common multiple, or LCM.

Common slips

Multiplying the two numbers. 4 × 6 = 24 is a common multiple of 4 and 6, but it is not the first one. Ask, "Is there a smaller number on both lists?"
Stopping too early. After 4, 8 and 6, there is no match yet. Ask, "Is any number on both lists?" before your child writes an answer.
Listing factors instead. If your child writes 1, 2 and 3 for "multiples of 6", ask, "Do multiples get bigger or smaller?"
A skip-counting slip. One wrong number spoils the rest of the list. Checking each match with a times-table fact, as in Step 4, catches it.

Three ways to practise at home

Paper, a pencil and a calendar are enough.

Crack the code. Write a "briefcase tag" for your child, such as "Code: the first common multiple of 3 and 5." Your child lists both and circles the match: 3, 6, 9, 12, 15 and 5, 10, 15, so the code is 15. Then swap roles and let your child set a code for you.
Calendar spies. On a month calendar, pick a start day for both activities. Mark every 4 days after it in one colour and every 6 days after it in another. The first day with both colours is 12 days after the start.
Hoot on the match. Take turns to skip-count in fours and in sixes, one list each. The first number that lands on both lists gets one quiet "Hoot." from whoever spots it.

Keep each session short and stop while your child still wants to play. When your child is stuck, ask "What comes next on this list?" before showing the answer, and praise the careful method rather than the speed.

Listing multiples leans on times tables, so if those still feel shaky, our guide to the 6, 7, 8 and 9 times tables shows a friendly way in.

Five calm questions a day

In the episode, the whole top-secret operation is five questions a day, each one announced by a hoot, while the day counter goes Day 1, Day 7, Day 30. It only ever goes up. Common multiples feel friendlier the same way: short lists, met often and checked with a method your child trusts.

That is the idea we built Singapore Math Drills around:

Daily Five drills: five hand-picked drill cards are waiting each day, so your child never has to decide what to practise.
Streaks: they reward turning up and getting things right, never speed.
Calm by design: no guilt-tripping over a missed day and no dark patterns. Your child's progress is only ever measured against their own.

Whole Numbers is one of our live Primary 4 topics, alongside Fractions and Decimals, the other two topics in the episode's mission file.

The Mastermind stays in character to the very last whisper, hugging his practice notebook: "Shh. Silent Owl."

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