Question : If A = 23 × 37, B = 27 × 35 and C = 28 × 34, then what is the least common multiple of A, B and C?
Option 1: 27× 37
Option 2: 26 × 37
Option 3: 28 × 37
Option 4: 29 × 37
Correct Answer: 2 8 × 3 7
Solution :
LCM is the product of Prime factors with the highest power
Here, the Prime factors are:
A = $2^3 \times 3^7$
B = $2^7 \times 3^5$
C = $2^8 \times 3^4$
The highest power for 2 is 2$^8$
The highest power for 3 is 3$^7$
$\therefore$ LCM = $2^8 \times 3^7$
Hence, the correct answer is 2
8
× 3
7
.
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