Euclid's Division Lemma Prime Factorisation Calculator Factors of a Number Calculator LCM Calculator GCF Calculator Factor Tree Calculator LCM of Decimals LCM of Fractions GCF of Decimals GCF of Fractions

Least Common Multiple of 10 and 15

Free LCM Calculator determines the least common multiple (LCM) between 10 and 15 the smallest integer that is 30 that is divisible by both numbers.

Least Common Multiple (LCM) of 10 and 15 is 30.

LCM(10,15) = 30

LCM of 10 and 15

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

LCM of:
and

Least Common Multiple (LCM) of 10 and 15 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 15. First we will calculate the prime factors of 10 and 15.

Prime Factorization of 10


2 10
5 5
1

Prime factors of 10 are 2,5. Prime factorization of 10 in exponential form is:

10 = 21×51

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 10 and 15.

LCM(10,15) = 21×31×51
LCM(10,15) = 30

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1, 2, 5, 10

Factors of 15

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

1, 3, 5, 15

Least Common Multiple of 10 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 10 and 15, than apply into the LCM equation.

GCF(10,15) = 5
LCM(10,15) = ( 10 × 15) / 5
LCM(10,15) = 150 / 5
LCM(10,15) = 30

Properties of LCM 10 and 15

(i) The LCM of 15 and 10 is associative

LCM of 10 and 15 = LCM of 15 and 10

Frequently Asked Questions on LCM of 10 and 15

1. What is the LCM of 10 and 15?

Answer: LCM of 10 and 15 is 30.

2. What are the Factors of 10?

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

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 10 and 15?

Answer:

Least Common Multiple of 10 and 15 = 30

Step 1: Find the prime factorization of 10

10 = 2 x 5

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 = 30 = 2 x 3 x 5

Step 4: Therefore, the least common multiple of 10 and 15 is 30.