Question

The L.C.M. of 33, 54, 108, 165, and 198 is:

• A. 4960
• B. 5010
• C. 5940
• D. 6010

Hint:

To find the L.C.M., always use the highest powers of all prime factors involved.

Answer 1

The Correct Option is C

To find the L.C.M., we first find the prime factorization of each number: \[ 33 = 3 \times 11, \quad 54 = 2 \times 3^3, \quad 108 = 2^2 \times 3^3, \quad 165 = 3 \times 5 \times 11, \quad 198 = 2 \times 3^2 \times 11. \] Now, the L.C.M. is found by taking the highest powers of each prime factor: \[ \text{L.C.M.} = 2^2 \times 3^3 \times 5 \times 11 = 5940. \] Thus, the L.C.M. of 33, 54, 108, 165, and 198 is 5940, which corresponds to option (3).