Discussion
The product of two numbers is 1764 and their HCF is 14. The LCM of these numbers is:
Answer: D
The LCM is 126. For two numbers, the product of the numbers equals the product of their HCF and their LCM.
\[ a \times b = \text{HCF} \times \text{LCM} \]
\[ \text{LCM} = \frac{1764}{14} = 126 \]
As a check, the LCM must be a multiple of the HCF. Now 126 = 14 x 9, which is a multiple of 14. The options 118, 120 and 124 are not multiples of 14, because 14 x 8 = 112 and 14 x 9 = 126, so none of them can be the LCM of two numbers whose HCF is 14.
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