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Least Common Multiple of 8 and 15

Free LCM Calculator determines the least common multiple (LCM) between 8 and 15 the smallest integer that is 120 that is divisible by both numbers.

Least Common Multiple (LCM) of 8 and 15 is 120.

LCM(8,15) = 120

LCM of 8 and 15

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

LCM of:
and

Least Common Multiple (LCM) of 8 and 15 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 15. First we will calculate the prime factors of 8 and 15.

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 15


3 15
5 5
1

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

15 = 31×51

Now multiplying the highest exponent prime factors to calculate the LCM of 8 and 15.

LCM(8,15) = 23×31×51
LCM(8,15) = 120

Factors of 8

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

1, 2, 4, 8

Factors of 15

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

1, 3, 5, 15

Least Common Multiple of 8 and 15 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 15, than apply into the LCM equation.

GCF(8,15) = 1
LCM(8,15) = ( 8 × 15) / 1
LCM(8,15) = 120 / 1
LCM(8,15) = 120

Least Common Multiple of 8 and 15 by Listing Multiples

Multiples of 8

8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112,120

Multiples of 15

15, 30, 45, 60, 75, 90, 105,120

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

∴ Least Common Multiple of 8 and 15 is 120

Properties of LCM 8 and 15

(i) The LCM of 15 and 8 is associative

LCM of 8 and 15 = LCM of 15 and 8

Frequently Asked Questions on LCM of 8 and 15

1. What is the LCM of 8 and 15?

Answer: LCM of 8 and 15 is 120.

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 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.

4. How to Find the LCM of 8 and 15?

Answer:

Least Common Multiple of 8 and 15 = 120

Step 1: Find the prime factorization of 8

8 = 2 x 2 x 2

Step 2: Find the prime factorization of 15

15 = 3 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 = 120 = 2 x 2 x 2 x 3 x 5

Step 4: Therefore, the least common multiple of 8 and 15 is 120.