# 21, 33 and 77 LCM LCM of 21, 33 and 77 is equal to 231. The comprehensive work provides more insight of how to find what is the lcm of 21, 33 and 77 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

what is the lcm of 21, 33 and 77?
lcm (21   33   77) = (?)
21 => 3 x 7
33 => 3 x 11
77 => 7 x 11

= 3 x 7 x 11
= 231
lcm (21, 33 and 77) = 231
231 is the lcm of 21, 33 and 77.

where,
21 is a positive integer,
33 is a positive integer,
231 is the lcm of 21, 33 and 77,
{3, 7, 11} in {3 x 7, 3 x 11, 7 x 11} are the most repeated factors of 21, 33 and 77,
There is no non-repeated factors of 21, 33 and 77 in {3 x 7, 3 x 11, 7 x 11}.

Use in Mathematics: LCM of 21, 33 and 77
The below are some of the mathematical applications where lcm of 21, 33 and 77 can be used:

1. to find the least number which is exactly divisible by 21, 33 and 77.
2. to find the common denominators for the fractions having 21, 33 and 77 as denominators in the unlike fractions addition or subtraction.
Use in Real-world Problems: 21, 33 and 77 lcm
In the context of lcm real world problems, the lcm of 21, 33 and 77 helps to find the exact time when three similar and recurring with different time schedule happens together at the same time. For example, the real world problems involve lcm in situations to find at what time all the bells A, B and C toll together, if bell A tolls at 21 seconds, B tolls at 33 seconds and C tolls at 77 seconds repeatedly. The answer is that all bells A, B and C toll together at 231 seconds for the first time, at 462 seconds for the second time, at 693 seconds for the third time and so on.

Important Notes: 21, 33 and 77 lcm
The below are the important notes to be remembered while solving the lcm of 21, 33 and 77:
1. The repeated and non-repeated prime factors of 21, 33 and 77 should be multiplied to find the least common multiple of 21, 33 and 77, when solving lcm by using prime factors method.
2. The results of lcm of 21, 33 and 77 is identical even if we change the order of given numbers in the lcm calculation, it means the order of given numbers in the lcm calculation doesn't affect the results.
For values other than 21, 33 and 77, use this below tool:

## How-to: What is the LCM of 21, 33 and 77?

The below solved example with step by step work shows how to find what is the lcm of 21, 33 and 77 by using either prime factors method and special division method.

Solved example using prime factors method:
What is the LCM of 21, 33 and 77?

step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 21
B = 33
C = 77

What to be found:
find the lcm of 21, 33 and 77

step 2 Find the prime factors of 21, 33 and 77:
Prime factors of 21 = 3 x 7
Prime factors of 33 = 3 x 11
Prime factors of 77 = 7 x 11

step 3 Identify the repeated and non-repeated prime factors of 21, 33 and 77:
{3, 7, 11} are the most repeated factors and there is no non-repeated factors of 21, 33 and 77.

step 4 Find the product of repeated and non-repeated prime factors of 21, 33 and 77:
= 3 x 7 x 11
= 231
lcm(20 and 30) = 231

Hence,
lcm of 21, 33 and 77 is 231

Solved example using special division method:
This special division method is the easiest way to understand the entire calculation of what is the lcm of 21, 33 and 77.

step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 21, 33 and 77

What to be found:
lcm (21, 33, 77) = ?

step 2 Arrange the given integers in the horizontal form with space or comma separated format:
21, 33 and 77

step 3 Choose the divisor which divides each or most of the given integers (21, 33 and 77), divide each integers separately and write down the quotient in the next line right under the respective integers. Bring down the integer to the next line if any integer in 21, 33 and 77 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

 3 21 33 77 7 7 11 77 11 1 11 11 1 1 1

step 4 Multiply the divisors to find the lcm of 21, 33 and 77:
= 3 x 7 x 11
= 231
LCM(21, 33, 77) = 231

The least common multiple for three numbers 21, 33 and 77 is 231 