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Least Common Multiple of 15 and 23

Free LCM Calculator determines the least common multiple (LCM) between 15 and 23 the smallest integer that is 345 that is divisible by both numbers.

Least Common Multiple (LCM) of 15 and 23 is 345.

LCM(15,23) = 345

LCM of 15 and 23

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

LCM of:
and

Least Common Multiple (LCM) of 15 and 23 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 15 and 23. First we will calculate the prime factors of 15 and 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

Prime Factorization of 23


23 23
1

Prime factors of 23 are 23. Prime factorization of 23 in exponential form is:

23 = 231

Now multiplying the highest exponent prime factors to calculate the LCM of 15 and 23.

LCM(15,23) = 31×51×231
LCM(15,23) = 345

Factors of 15

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

1, 3, 5, 15

Factors of 23

List of positive integer factors of 23 that divides 23 without a remainder.

1, 23

Least Common Multiple of 15 and 23 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 23, than apply into the LCM equation.

GCF(15,23) = 1
LCM(15,23) = ( 15 × 23) / 1
LCM(15,23) = 345 / 1
LCM(15,23) = 345

Properties of LCM 15 and 23

(i) The LCM of 23 and 15 is associative

LCM of 15 and 23 = LCM of 23 and 15

Frequently Asked Questions on LCM of 15 and 23

1. What is the LCM of 15 and 23?

Answer: LCM of 15 and 23 is 345.

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 23?

Answer: Factors of 23 are 1, 23. There are 2 integers that are factors of 23. The greatest factor of 23 is 23.

4. How to Find the LCM of 15 and 23?

Answer:

Least Common Multiple of 15 and 23 = 345

Step 1: Find the prime factorization of 15

15 = 3 x 5

Step 2: Find the prime factorization of 23

23 = 23

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

LCM = 345 = 3 x 5 x 23

Step 4: Therefore, the least common multiple of 15 and 23 is 345.