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Least Common Multiple of 14 and 20

Free LCM Calculator determines the least common multiple (LCM) between 14 and 20 the smallest integer that is 140 that is divisible by both numbers.

Least Common Multiple (LCM) of 14 and 20 is 140.

LCM(14,20) = 140

LCM of 14 and 20

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple (LCM) of 14 and 20 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14 and 20. First we will calculate the prime factors of 14 and 20.

Prime Factorization of 14


2 14
7 7
1

Prime factors of 14 are 2,7. Prime factorization of 14 in exponential form is:

14 = 21×71

Prime Factorization of 20


2 20
2 10
5 5
1

Prime factors of 20 are 2,5. Prime factorization of 20 in exponential form is:

20 = 22×51

Now multiplying the highest exponent prime factors to calculate the LCM of 14 and 20.

LCM(14,20) = 22×51×71
LCM(14,20) = 140

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1, 2, 7, 14

Factors of 20

List of positive integer factors of 20 that divides 20 without a remainder.

1, 2, 4, 5, 10, 20

Least Common Multiple of 14 and 20 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14 and 20, than apply into the LCM equation.

GCF(14,20) = 2
LCM(14,20) = ( 14 × 20) / 2
LCM(14,20) = 280 / 2
LCM(14,20) = 140

Properties of LCM 14 and 20

(i) The LCM of 20 and 14 is associative

LCM of 14 and 20 = LCM of 20 and 14

Frequently Asked Questions on LCM of 14 and 20

1. What is the LCM of 14 and 20?

Answer: LCM of 14 and 20 is 140.

2. What are the Factors of 14?

Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.

3. What are the Factors of 20?

Answer: Factors of 20 are 1, 2, 4, 5, 10, 20. There are 6 integers that are factors of 20. The greatest factor of 20 is 20.

4. How to Find the LCM of 14 and 20?

Answer:

Least Common Multiple of 14 and 20 = 140

Step 1: Find the prime factorization of 14

14 = 2 x 7

Step 2: Find the prime factorization of 20

20 = 2 x 2 x 5

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 140 = 2 x 2 x 5 x 7

Step 4: Therefore, the least common multiple of 14 and 20 is 140.