Least Common Multiple of 8 and 20

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 8 and 20 the smallest integer that is 40 that is divisible by both numbers.

Least Common Multiple (LCM) of 8 and 20 is 40.

LCM(8,20) = 40

LCM of 8 and 20

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

LCM of:
and

Least Common Multiple of 8 and 20

LCM of 8 and 20 is 40

Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 20. First we will calculate the prime factors of 8 and 20.

Prime Factorization of 8


2 8
2 4
2 2
1

Prime factors of 8 are 2. Prime factorization of 8 in exponential form is:

8 = 23

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 8 and 20.

LCM(8,20) = 23×51
LCM(8,20) = 40

Factors of 8

List of positive integer factors of 8 that divides 8 without a remainder.

1, 2, 4, 8

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 8 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 8 and 20, than apply into the LCM equation.

GCF(8,20) = 4
LCM(8,20) = ( 8 × 20) / 4
LCM(8,20) = 160 / 4
LCM(8,20) = 40

Properties of LCM 8 and 20

(i) The LCM of 20 and 8 is associative

LCM of 8 and 20 = LCM of 20 and 8

Related Least Common Multiples of 8

Related Least Common Multiples of 20

Frequently Asked Questions on LCM of 8 and 20

1. What is the LCM of 8 and 20?

Answer: LCM of 8 and 20 is 40.

2. What are the Factors of 8?

Answer: Factors of 8 are 1, 2, 4, 8. There are 4 integers that are factors of 8. The greatest factor of 8 is 8.

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 8 and 20?

Answer:

Least Common Multiple of 8 and 20 = 40

Step 1: Find the prime factorization of 8

8 = 2 x 2 x 2

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 = 40 = 2 x 2 x 2 x 5

Step 4: Therefore, the least common multiple of 8 and 20 is 40.