Least Common Multiple of 21 and 23

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

• Least Common Multiple of 21 and 23 by Prime method
• Least Common Multiple of 21 and 23 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 23. First we will calculate the prime factors of 21 and 23.

Prime Factorization of 21

Prime factors of 21 are 3,7. Prime factorization of 21 in exponential form is:

21 = 3¹×7¹

Prime Factorization of 23

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 21 and 23.

LCM(21,23) = 3¹×7¹×23¹
LCM(21,23) = 483

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1, 3, 7, 21

Factors of 23

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

1, 23

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21 and 23, than apply into the LCM equation.

GCF(21,23) = 1
LCM(21,23) = ( 21 × 23) / 1
LCM(21,23) = 483 / 1
LCM(21,23) = 483

(i) The LCM of 23 and 21 is associative

LCM of 21 and 23 = LCM of 23 and 21

1. What is the LCM of 21 and 23?

Answer: LCM of 21 and 23 is 483.

2. What are the Factors of 21?

Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.

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 21 and 23?

Answer:

Least Common Multiple of 21 and 23 = 483

Step 1: Find the prime factorization of 21

21 = 3 x 7

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 = 483 = 3 x 7 x 23

Step 4: Therefore, the least common multiple of 21 and 23 is 483.