Least Common Multiple of 15 and 16

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 15 and 16 the smallest integer that is 240 that is divisible by both numbers.

Least Common Multiple (LCM) of 15 and 16 is 240.

LCM(15,16) = 240

LCM of 15 and 16

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

LCM of:
and

Least Common Multiple of 15 and 16

LCM of 15 and 16 is 240

Least common multiple can be found by multiplying the highest exponent prime factors of 15 and 16. First we will calculate the prime factors of 15 and 16.

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 16


2 16
2 8
2 4
2 2
1

Prime factors of 16 are 2. Prime factorization of 16 in exponential form is:

16 = 24

Now multiplying the highest exponent prime factors to calculate the LCM of 15 and 16.

LCM(15,16) = 24×31×51
LCM(15,16) = 240

Factors of 15

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

1, 3, 5, 15

Factors of 16

List of positive integer factors of 16 that divides 16 without a remainder.

1, 2, 4, 8, 16

Least Common Multiple of 15 and 16 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 16, than apply into the LCM equation.

GCF(15,16) = 1
LCM(15,16) = ( 15 × 16) / 1
LCM(15,16) = 240 / 1
LCM(15,16) = 240

Properties of LCM 15 and 16

(i) The LCM of 16 and 15 is associative

LCM of 15 and 16 = LCM of 16 and 15

Related Least Common Multiples of 15

Related Least Common Multiples of 16

Frequently Asked Questions on LCM of 15 and 16

1. What is the LCM of 15 and 16?

Answer: LCM of 15 and 16 is 240.

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 16?

Answer: Factors of 16 are 1, 2, 4, 8, 16. There are 5 integers that are factors of 16. The greatest factor of 16 is 16.

4. How to Find the LCM of 15 and 16?

Answer:

Least Common Multiple of 15 and 16 = 240

Step 1: Find the prime factorization of 15

15 = 3 x 5

Step 2: Find the prime factorization of 16

16 = 2 x 2 x 2 x 2

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

LCM = 240 = 2 x 2 x 2 x 2 x 3 x 5

Step 4: Therefore, the least common multiple of 15 and 16 is 240.