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Least Common Multiple of 15 and 20

Free LCM Calculator determines the least common multiple (LCM) between 15 and 20 the smallest integer that is 60 that is divisible by both numbers.

Least Common Multiple (LCM) of 15 and 20 is 60.

LCM(15,20) = 60

LCM of 15 and 20

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

LCM of:
and

Least Common Multiple (LCM) of 15 and 20 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 15 and 20. First we will calculate the prime factors of 15 and 20.

Prime Factorization of 15


3 15
5 5
1

Prime factors of 15 are 3,5. Prime factorization of 15 in exponential form is:

15 = 31×51

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 15 and 20.

LCM(15,20) = 22×31×51
LCM(15,20) = 60

Factors of 15

List of positive integer factors of 15 that divides 15 without a remainder.

1, 3, 5, 15

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 15 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 15 and 20, than apply into the LCM equation.

GCF(15,20) = 5
LCM(15,20) = ( 15 × 20) / 5
LCM(15,20) = 300 / 5
LCM(15,20) = 60

Least Common Multiple of 15 and 20 by Listing Multiples

Multiples of 15

15, 30, 45,60

Multiples of 20

20, 40,60

Find the smallest number that is on all of the lists. We have it in bold above.

∴ Least Common Multiple of 15 and 20 is 60

Properties of LCM 15 and 20

(i) The LCM of 20 and 15 is associative

LCM of 15 and 20 = LCM of 20 and 15

Frequently Asked Questions on LCM of 15 and 20

1. What is the LCM of 15 and 20?

Answer: LCM of 15 and 20 is 60.

2. What are the Factors of 15?

Answer: Factors of 15 are 1, 3, 5, 15. There are 4 integers that are factors of 15. The greatest factor of 15 is 15.

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 15 and 20?

Answer:

Least Common Multiple of 15 and 20 = 60

Step 1: Find the prime factorization of 15

15 = 3 x 5

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 = 60 = 2 x 2 x 3 x 5

Step 4: Therefore, the least common multiple of 15 and 20 is 60.