Discussion
If LCM of two numbers is 392, then which of the following cannot be the HCF of these numbers?
Answer: B
The number that cannot be the HCF is 42.
The HCF of two numbers always divides their LCM, because both numbers divide the LCM and the HCF divides both numbers. Factorise the LCM:
\[ 392 = 2^{3} \times 7^{2} \]
Now test the options: 28 = 22 × 7, 56 = 23 × 7 and 196 = 22 × 72 all divide 392, so each could be the HCF. But 42 = 2 × 3 × 7 contains the prime 3, which 392 does not, so 42 does not divide 392 and cannot be the HCF.
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