LCM of 42, 48 and 56 is equal to 336. The comprehensive work provides more insight of how to find what is the lcm of 42, 48 and 56 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

__what is the lcm of 42, 48 and 56?__

lcm (42 48 56) = (?)

42 => 2 x 3 x 7

48 => 2 x 2 x 2 x 2 x 3

56 => 2 x 2 x 2 x 7

= 2 x 2 x 2 x 3 x 7 x 2

= 336

lcm (42, 48 and 56) = 336

336 is the lcm of 42, 48 and 56.

__where,__

42 is a positive integer,

48 is a positive integer,

336 is the lcm of 42, 48 and 56,

{2, 2, 2, 3, 7} in {2 x 3 x 7, 2 x 2 x 2 x 2 x 3, 2 x 2 x 2 x 7} are the most repeated factors of 42, 48 and 56,

{2} in {2 x 3 x 7, 2 x 2 x 2 x 2 x 3, 2 x 2 x 2 x 7} is the other remaining factors of 42, 48 and 56.

__Use in Mathematics: LCM of 42, 48 and 56__

The below are some of the mathematical applications where lcm of 42, 48 and 56 can be used:

- to find the least number which is exactly divisible by 42, 48 and 56.
- to find the common denominators for the fractions having 42, 48 and 56 as denominators in the unlike fractions addition or subtraction.

In the context of lcm real world problems, the lcm of 42, 48 and 56 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 42 seconds, B tolls at 48 seconds and C tolls at 56 seconds repeatedly. The answer is that all bells A, B and C toll together at 336 seconds for the first time, at 672 seconds for the second time, at 1008 seconds for the third time and so on.

The below are the important notes to be remembered while solving the lcm of 42, 48 and 56:

- The repeated and non-repeated prime factors of 42, 48 and 56 should be multiplied to find the least common multiple of 42, 48 and 56, when solving lcm by using prime factors method.
- The results of lcm of 42, 48 and 56 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.

The below solved example with step by step work shows how to find what is the lcm of 42, 48 and 56 by using either prime factors method and special division method.

__Solved example using prime factors method:__

What is the LCM of 42, 48 and 56?

step 1
Address the input parameters, values and observe what to be found:

__Input parameters and values:__

A = 42

B = 48

C = 56

__What to be found:__

find the lcm of 42, 48 and 56

step 2 Find the prime factors of 42, 48 and 56:

Prime factors of 42 = 2 x 3 x 7

Prime factors of 48 = 2 x 2 x 2 x 2 x 3

Prime factors of 56 = 2 x 2 x 2 x 7

step 3 Identify the repeated and non-repeated prime factors of 42, 48 and 56:

{2, 2, 2, 3, 7} are the most repeated factors and {2} is the non-repeated factors of 42, 48 and 56.

step 4 Find the product of repeated and non-repeated prime factors of 42, 48 and 56:

= 2 x 2 x 2 x 3 x 7 x 2

= 336

lcm(20 and 30) = 336

Hence,

lcm of 42, 48 and 56 is 336

This special division method is the easiest way to understand the entire calculation of what is the lcm of 42, 48 and 56.

step 1 Address the input parameters, values and observe what to be found:

Integers: 42, 48 and 56

lcm (42, 48, 56) = ?

step 2 Arrange the given integers in the horizontal form with space or comma separated format:

42, 48 and 56

step 3 Choose the divisor which divides each or most of the given integers (42, 48 and 56), 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 42, 48 and 56 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

2 | 42 | 48 | 56 |

2 | 21 | 24 | 28 |

2 | 21 | 12 | 14 |

2 | 21 | 6 | 7 |

3 | 21 | 3 | 7 |

7 | 7 | 1 | 7 |

1 | 1 | 1 |

step 4 Multiply the divisors to find the lcm of 42, 48 and 56:

= 2 x 2 x 2 x 2 x 3 x 7

= 336

LCM(42, 48, 56) = 336

The least common multiple for three numbers 42, 48 and 56 is 336