Lesson 10 of 14
HCF and LCM of three numbers
Show on a big screenTwo numbers have an HCF and an LCM. So do three. The HCF is the highest common factor. The LCM is the lowest common multiple.
18 = 2 × 3², 30 = 2 × 3 × 5, 45 = 3² × 5. The table shows each power. Step 1 of 4
- Write 18, 30 and 45 as primes:
18 = 2 × 3²,30 = 2 × 3 × 5,45 = 3² × 5. The table shows each power. - HCF: take the smallest power of each prime. That gives
3¹, so the HCF is 3. - LCM: take the greatest power of each prime. That gives
2 × 3² × 5, so the LCM is 90. - HCF × LCM = 270. But 18 × 30 × 45 = 24300. They differ.
The rule
Count a missing prime as power 0. HCF takes the smallest power of each prime. LCM takes the greatest.
The prime 2 is missing from 45. So 45 has 2 to the power 0 there. The smallest power of 2 is 0. So 2 is not in the HCF.
For two numbers, HCF × LCM is their product. For three numbers it can differ. With 2, 3 and 5 they match: 1 × 30 = 30.
| Number | In primes | Power of 2 | Power of 3 | Power of 7 |
|---|---|---|---|---|
| 28 | 2² × 7 | 2 | 0 | 1 |
| 42 | 2 × 3 × 7 | 1 | 1 | 1 |
| 63 | 3² × 7 | 0 | 2 | 1 |
| HCF | 7 | 0 | 0 | 1 |
| LCM | 2² × 3² × 7 | 2 | 2 | 1 |
HCF = 7. LCM = 4 × 9 × 7 = 252.
Now try it. Tap the HCF and then the LCM.
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Try the lab to finish this lesson.