Math worksheet for finding the least common multiple (LCM) of number pairs.

Let’s solve each problem step by step using the same method shown in example #1: prime factorization with a division table, then multiply all the divisors and remaining numbers to get the LCM.

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Problem 3: (12, 30)

We’ll divide both numbers by common prime factors until we can’t anymore.

Start with 2:
- 12 ÷ 2 = 6
- 30 ÷ 2 = 15
→ Write down 2 on the left.

Now try 2 again? 6 is divisible by 2, but 15 is not → skip.

Try 3:
- 6 ÷ 3 = 2
- 15 ÷ 3 = 5
→ Write down 3 on the left.

Now we have 2 and 5 — no more common factors.

So the divisors used: 2, 3
Remaining numbers: 2, 5

LCM = 2 × 3 × 2 × 5 = 60

✔ Check: Multiples of 12: 12, 24, 36, 48, 60...
Multiples of 30: 30, 60... → Yes, 60 is the least common multiple.

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Problem 4: (15, 25)

Start with smallest prime that divides both: 5

- 15 ÷ 5 = 3
- 25 ÷ 5 = 5
→ Write down 5.

Now we have 3 and 5 — no common factors.

Divisors: 5
Remaining: 3, 5

LCM = 5 × 3 × 5 = 75

✔ Check: Multiples of 15: 15, 30, 45, 60, 75...
Multiples of 25: 25, 50, 75... → Correct.

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Problem 5: (30, 10)

Note: 10 divides into 30 evenly. So LCM should be 30.

But let’s do it properly:

Start with 2:
- 30 ÷ 2 = 15
- 10 ÷ 2 = 5
→ Write 2.

Now 15 and 5 — try 5:
- 15 ÷ 5 = 3
- 5 ÷ 5 = 1
→ Write 5.

Left with 3 and 1.

Divisors: 2, 5
Remaining: 3, 1

LCM = 2 × 5 × 3 × 1 = 30

✔ Makes sense — since 30 is a multiple of 10, LCM is 30.

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Problem 6: (25, 45)

Start with 5:
- 25 ÷ 5 = 5
- 45 ÷ 5 = 9
→ Write 5.

Again, 5 and 9 — 5 doesn’t divide 9, so stop dividing by 5.

No other common primes.

Divisors: 5
Remaining: 5, 9

LCM = 5 × 5 × 9 = 225

✔ Check:
Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225...
Multiples of 45: 45, 90, 135, 180, 225... → Yes, 225 is correct.

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Final Answer:

3. 60
4. 75
5. 30
6. 225