Question

1. The LCM of (48) and (* 6) is 144. Which number should replace * ?

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Answer 1

Answer:

Recall the definition of LCM (least common multiple) must be divisible by the given numbers. Factorize given numbers

48=2×2×2×2×3

144=2×2×2×2×3×3

Since 48 has only one factor 3 hence the unknown number say x must have at least 3×3=9 as its factor(s) so possible unknown number may be

x=3×3=9

or x=2×3×3=18

or x=2×2×3×3=36

or x=2×2×2×3×3=72

or x=2×2×2×2×3×3=144

So the unknown number x may have any value such that x∈{9,18,36,72,144}