Question : Find the LCM of 15, 24, 35 and 54.
Option 1: 5670
Option 2: 7560
Option 3: 7650
Option 4: 6570
Correct Answer: 7560
Solution :
The LCM (Least Common Multiple) of 15, 24, 35, and 54 can be found using the prime factorization method.
Prime factorization of 15 = $3^1 \times 5^1$
Prime factorization of 24 = $2^3 \times 3^1$
Prime factorization of 35 = $5^1 \times 7^1$
Prime factorization of 54 = $2^1 \times 3^3$
Now, we take the highest power of each prime number:
The highest power of 2 = $2^3$
The highest power of 3 = $3^3$
The highest power of 5 = $5^1$
The highest power of 7 = $7^1$
Multiply these together to get the LCM = $2^3 \times 3^3 \times 5^1 \times 7^1 = 7560$
Hence, the correct answer is 7560.
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