QA – Placement Quizzes | Numbers, LCM and HCF | Question 4

What is the total number of prime factors in the expression 12¹² x 16¹⁶ x 18¹⁸ ?
(A) 46
(B) 154
(C) 3456
(D) 2


Answer: (B)

Explanation: 12¹² = (2 x 2 x 3)¹² = 2²⁴ x 3¹²
16¹⁶ = (2 x 2 x 2 x 2)¹⁶ = 2⁶⁴
18¹⁸ = (2 x 3 x 3)¹⁸ = 2¹⁸ x 3³⁶

Therefore, total number of prime factors = 24 + 12 + 64 + 18 + 36 = 154

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