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Least Common Multiple of 18 and 23

Free LCM Calculator determines the least common multiple (LCM) between 18 and 23 the smallest integer that is 414 that is divisible by both numbers.

Least Common Multiple (LCM) of 18 and 23 is 414.

LCM(18,23) = 414

LCM of 18 and 23

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

LCM of:
and

Least Common Multiple (LCM) of 18 and 23 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 18 and 23. First we will calculate the prime factors of 18 and 23.

Prime Factorization of 18


2 18
3 9
3 3
1

Prime factors of 18 are 2,3. Prime factorization of 18 in exponential form is:

18 = 21×32

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 18 and 23.

LCM(18,23) = 21×32×231
LCM(18,23) = 414

Factors of 18

List of positive integer factors of 18 that divides 18 without a remainder.

1, 2, 3, 6, 9, 18

Factors of 23

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

1, 23

Least Common Multiple of 18 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 18 and 23, than apply into the LCM equation.

GCF(18,23) = 1
LCM(18,23) = ( 18 × 23) / 1
LCM(18,23) = 414 / 1
LCM(18,23) = 414

Properties of LCM 18 and 23

(i) The LCM of 23 and 18 is associative

LCM of 18 and 23 = LCM of 23 and 18

Frequently Asked Questions on LCM of 18 and 23

1. What is the LCM of 18 and 23?

Answer: LCM of 18 and 23 is 414.

2. What are the Factors of 18?

Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.

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 18 and 23?

Answer:

Least Common Multiple of 18 and 23 = 414

Step 1: Find the prime factorization of 18

18 = 2 x 3 x 3

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 = 414 = 2 x 3 x 3 x 23

Step 4: Therefore, the least common multiple of 18 and 23 is 414.