LCM of 16 and 42

LCM of 16 and 42 is 336. LCM is abbreviated as Least Common multiple or Lowest common multiple. LCM is the simplest method to find out the smallest common multiples between two or more numbers.

The LCM of 16 and 42, is the smallest number among all the common multiples of 16 and 42.

What is the LCM of 16 and 42

The Least Common Multiple or Lowest Common Multiple of 16 and 42 is 336.

LCM of 16 and 42

How to Find LCM of 16 and 42?

Let us see the different methods for finding the LCM of 16 and 42.

  • By Prime Factorisation
  • By Division method
  • By Listing the multiples

LCM of 16 and 42 Using Prime Factorisation Method

Let us find the LCM of 16 and 42 by the Prime Factorisation Method. The steps are as follows:

Step 1: Find the Prime factorisation of 16

16 = 2 x 2 x 2 x 2

Step 2: Find the Prime factorisation of 42

42 = 2 x 3 x 7

Step 3: Multiply each factor the greater number of times it occurs

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

Step 4 : LCM = 336

LCM of 16 and 42 by division method

To Calculate the LCM of 16 and 42 by the division method, we will divide the numbers 16 and 42 by their prime factors. The Product of these divisors gives the LCM of 16 and 42.

Let us see the steps to follow:

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 16 and 42.

Step 2: If any of the given numbers 16 or 42 is a multiple of 2, divide it by 2 and write the quotient below it. Bring down the number as it is, if it is not divisible by the prime number

Step3: Continue these steps until you get only 1s in the last row.

The LCM of 16 and 42 by division method is 336.

2 16 42
2 8 21
2 4 21
2 2 21
3 1 21
7 1 7
x 1 1

LCM= 2 × 2 × 2 × 2 × 3 × 7 = 336

LCM of 16 and 42 by Listing Multiples

To Calculate the LCM of 16 and 42, let us list the multiples of 16 and 42

Multiples of 16 : 16,32,48,64,80,96..

Multiples of 42 : 42,84,126,168..

Step 1: List out a few multiples of 16 and 42

Step 2: Now the common multiples from the multiples of 16 and 42 are 336,672

Step 3: The smallest common multiple of 16 and 42 is 336.

Hence the least common multiple of 16 and 42 = 336

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Solved Examples

Example 1:

Find the smallest number that is divisible by 16 and 42 exactly?

Solution:

The smallest number that is divisible by 16 and 42 exactly is their LCM

Therefore, the LCM of 16 and 42 is 336

Example 2:

Which of the following is the LCM of 16 and 42?

a) 336 b)12 c)40 d)18

Solution:

The LCM of 16 and 42 is 336

Frequently Asked Questions on LCM of 16 and 42

Q1

What is the LCM of 16 and 42?

The LCM of 16 and 42 is 336.
Q2

How many methods are there to find the LCM?

There are three common methods to find LCM.
Q3

Which method is easy and fast to find out the LCM?

The easiest and fastest method to find the LCM of numbers is the listing of multiples method.

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