The problem states that when a number x is divided by 30, 45, or 54, the remainder is always 21. This means that x - 21 must be a multiple of 30, 45, and 54. To find the least value of x, we n

The problem states that when a number $x$ is divided by 30, 45, or 54, the remainder is always 21. This means that $x - 21$ must be a multiple of 30, 45, and 54. To find the least value of $x$, we need to find the least common multiple (LCM) of 30, 45, and 54.

• For 30:

• For 45:

• For 54:

To find the LCM, take the highest power of each prime factor present in any of the numbers:

• Highest power of 2: $2^1$
• Highest power of 3: $3^3$
• Highest power of 5: $5^1$

We know that $x - 21$ is the LCM.

Add 21 to both sides to find $x$:

The least value of the number $x$ is $\boxed{\textbf{291}}$.