Least Common Multiple of 23 and 28

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

• Least Common Multiple of 23 and 28 by Prime method
• Least Common Multiple of 23 and 28 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 23 and 28. First we will calculate the prime factors of 23 and 28.

Prime Factorization of 23

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

23 = 23¹

Prime Factorization of 28

Prime factors of 28 are 2,7. Prime factorization of 28 in exponential form is:

28 = 2²×7¹

Now multiplying the highest exponent prime factors to calculate the LCM of 23 and 28.

LCM(23,28) = 2²×7¹×23¹
LCM(23,28) = 644

Factors of 23

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

1, 23

Factors of 28

List of positive integer factors of 28 that divides 28 without a remainder.

1, 2, 4, 7, 14, 28

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 23 and 28, than apply into the LCM equation.

GCF(23,28) = 1
LCM(23,28) = ( 23 × 28) / 1
LCM(23,28) = 644 / 1
LCM(23,28) = 644

(i) The LCM of 28 and 23 is associative

LCM of 23 and 28 = LCM of 28 and 23

1. What is the LCM of 23 and 28?

Answer: LCM of 23 and 28 is 644.

2. 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.

3. What are the Factors of 28?

Answer: Factors of 28 are 1, 2, 4, 7, 14, 28. There are 6 integers that are factors of 28. The greatest factor of 28 is 28.

4. How to Find the LCM of 23 and 28?

Answer:

Least Common Multiple of 23 and 28 = 644

Step 1: Find the prime factorization of 23

23 = 23

Step 2: Find the prime factorization of 28

28 = 2 x 2 x 7

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

LCM = 644 = 2 x 2 x 7 x 23

Step 4: Therefore, the least common multiple of 23 and 28 is 644.