LCM of 14 and 20
The lowest number among all common multiples of 14 and 20 is the LCM of 14 and 20 (LCM of 14 and 20). The initial few multiples of 14 and 20 are 14, 28, 42, 56, 70, and 20, 40, 60, 80, respectively. We will now examine the techniques for determining the LCM of 14 and 20, including prime factorization and listing multiples.
What is LCM of 14 and 20?
140 is the Least Common Multiple or Lowest Common Multiple of 14 and 20.
LCM of 14 and 20 Using Prime Factorisation Method
As we know,
Prime factorization of 14 is known to be (2 × 7) = 21 × 71
Prime factorization of 20 is known to be (2 × 2 × 5) = 22 × 51 respectively.
By multiplying prime factors up to their corresponding greatest power, we can find the LCM of 14 and 20.
i.e. 22 × 51 × 71 = 140.
As a result, 140 is the LCM of 14 and 20 using prime factorization.
LCM of 14 and 20 Using Listing the Multiples
We can identify the least common multiple, or LCM, by compiling a list of all the multiples of the provided integers. The list of multiples for 14 and 20 is below.
- 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, … are all multiples of 14.
- 20, 40, 60, 80, 100, 120, 140, 160, 180, … are multiples of 20.
Therefore, LCM (14, 20) = 140.
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Solved Examples on LCM of 14 and 20
Example 1:
Find the lowest integer that is exactly divisible by 14 and 20.
Solution:
The LCM is the smallest number that is exactly divisible by both 14 and 20.
Here are the multiples of 14 and 20:
Multiples of 14 are 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, . . . .
Multiples of 20 are 20, 40, 60, 80, 100, 120, 140, . . . .
Hence, the LCM of 14 and 20 is 140.
Example 2:
280 is the result of multiplying two integers. What is their LCM if their GCD is 2?
Solution:
Given that, GCD = 2
Also, given that the product of numbers = 280
We know that, LCM × GCD = product of numbers
Now, rearrange the formula and substitute the given values,
⇒ LCM = Product/GCD
LCM = 280/2
Hence, the LCM is 140.
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