Find the HCF and the LCM of 28, 42 and 70. Is HCF × LCM equal to 28 × 42 × 70?

Step 1. Factorise. $28 = 2^2 \times 7$, $42 = 2 \times 3 \times 7$, $70 = 2 \times 5 \times 7$.

Step 2. HCF. Only $2$ and $7$ are in all three, with smallest powers $2^1$ and $7^1$: HCF $= 14$.

Step 3. LCM. All primes with greatest powers: $2^2 \times 3 \times 5 \times 7 = 420$.

Step 4. The product. $14 \times 420 = 5880$, but $28 \times 42 \times 70 = 82\,320$. They are not equal: the rule is for two numbers only.