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.
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
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