HCF and LCM of three numbers
Two 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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