LCM of 32, 64 and 68

LCM of 32, 64 and 68 is equal to 1088. The comprehensive work provides more insight of how to find what is the lcm of 32, 64 and 68 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

what is the lcm of 32, 64 and 68?
lcm (32 64 68) = (?)
32 => 2 x 2 x 2 x 2 x 2
64 => 2 x 2 x 2 x 2 x 2 x 2
68 => 2 x 2 x 17

= 2 x 2 x 2 x 2 x 2 x 2 x 17
= 1088
lcm (32, 64 and 68) = 1088
1088 is the lcm of 32, 64 and 68.

where,
32 is a positive integer,
64 is a positive integer,
1088 is the lcm of 32, 64 and 68,
{2, 2, 2, 2, 2} in {2 x 2 x 2 x 2 x 2, 2 x 2 x 2 x 2 x 2 x 2, 2 x 2 x 17} are the most repeated factors of 32, 64 and 68,
{2, 17} in {2 x 2 x 2 x 2 x 2, 2 x 2 x 2 x 2 x 2 x 2, 2 x 2 x 17} are the the other remaining factors of 32, 64 and 68.

Use in Mathematics: LCM of 32, 64 and 68
The below are some of the mathematical applications where lcm of 32, 64 and 68 can be used:

to find the least number which is exactly divisible by 32, 64 and 68.
to find the common denominators for the fractions having 32, 64 and 68 as denominators in the unlike fractions addition or subtraction.

Use in Real-world Problems: 32, 64 and 68 lcm
In the context of lcm real world problems, the lcm of 32, 64 and 68 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 32 seconds, B tolls at 64 seconds and C tolls at 68 seconds repeatedly. The answer is that all bells A, B and C toll together at 1088 seconds for the first time, at 2176 seconds for the second time, at 3264 seconds for the third time and so on.

Important Notes: 32, 64 and 68 lcm
The below are the important notes to be remembered while solving the lcm of 32, 64 and 68:

The repeated and non-repeated prime factors of 32, 64 and 68 should be multiplied to find the least common multiple of 32, 64 and 68, when solving lcm by using prime factors method.
The results of lcm of 32, 64 and 68 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 32, 64 and 68, use this below tool:

The below solved example with step by step work shows how to find what is the lcm of 32, 64 and 68 by using either prime factors method and special division method.

Solved example using prime factors method:
What is the LCM of 32, 64 and 68?

step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 32
B = 64
C = 68

What to be found:
find the lcm of 32, 64 and 68

step 2 Find the prime factors of 32, 64 and 68:
Prime factors of 32 = 2 x 2 x 2 x 2 x 2
Prime factors of 64 = 2 x 2 x 2 x 2 x 2 x 2
Prime factors of 68 = 2 x 2 x 17

step 3 Identify the repeated and non-repeated prime factors of 32, 64 and 68:
{2, 2, 2, 2, 2} are the most repeated factors and {2, 17} are the non-repeated factors of 32, 64 and 68.

step 4 Find the product of repeated and non-repeated prime factors of 32, 64 and 68:
= 2 x 2 x 2 x 2 x 2 x 2 x 17
= 1088
lcm(20 and 30) = 1088

Hence,
lcm of 32, 64 and 68 is 1088

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 32, 64 and 68.

step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 32, 64 and 68

What to be found:
lcm (32, 64, 68) = ?

step 2 Arrange the given integers in the horizontal form with space or comma separated format:
32, 64 and 68

step 3 Choose the divisor which divides each or most of the given integers (32, 64 and 68), 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 32, 64 and 68 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

2	32	64	68
2	16	32	34
2	8	16	17
2	4	8	17
2	2	4	17
2	1	2	17
17	1	1	17
	1	1	1

step 4 Multiply the divisors to find the lcm of 32, 64 and 68:
= 2 x 2 x 2 x 2 x 2 x 2 x 17
= 1088
LCM(32, 64, 68) = 1088

The least common multiple for three numbers 32, 64 and 68 is 1088

32, 64 and 68 LCM

How-to: What is the LCM of 32, 64 and 68?