LCM of 27 and 63:

The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is a multiple of all the numbers. To find the LCM of 27 and 63, we can use prime factorization.

• First, factorize each number: 27 = 3 x 3 x 3 = 33 and 63 = 3 x 3 x 7 = 32 x 7.
• To find the LCM, take the highest power of all prime factors present in either number: 33 x 7 = 27 x 7 = 189.

Therefore, 189 is the smallest number that is divisible by both 27 and 63.

• Options B (54), C (81), and D (126) are multiples of one number but not both, or not the least common multiple. For instance, 54 is 27 x 2 but not a multiple of 63.