Question

Find the LCM of the following numbers by the common division method.

33, 55, 100

Accepted Answer

The given numbers are $33, 55, 100$ .

The LCM of two or more numbers is the smallest number that can be divided by all the given numbers.

Steps to find LCM by the common division method.

(i) Divide by the least prime number which divides at least one of the numbers.

(ii) Write the quotient in the second row. Also, write the number(s) that cannot be divided by this prime number in the second row.

(iii) Again, divide by the same prime number or the next bigger prime number which divides at least one of the numbers.

(iv) Write the quotient in the third row. Also, write the number(s) that cannot be divided by this prime number in the third row.

(v) Repeat the process with the next rows and continue till all the numbers in a row are $1$ .

(vi) Now, multiply all the prime divisors to find the LCM.

Thus, we have,

$\begin{matrix} 2 & 33, & 55, & 100 \\ 2 & 33, & 55, & 50 \\ 3 & 33, & 55, & 25 \\ 5 & 11, & 55, & 25 \\ 5 & 11, & 11, & 5 \\ 11 & 11, & 11, & 1 \\ 1, & 1, & 1 \end{matrix}$

The LCM of the three numbers $= 2 \times 2 \times 3 \times 5 \times 5 \times 11 = 3300$ .

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