Least Common Multiple of 21 and 33

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 21 and 33 the smallest integer that is 231 that is divisible by both numbers.

Least Common Multiple (LCM) of 21 and 33 is 231.

LCM(21,33) = 231

LCM of 21 and 33

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

LCM of:
and

Least Common Multiple of 21 and 33

LCM of 21 and 33 is 231

Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 33. First we will calculate the prime factors of 21 and 33.

Prime Factorization of 21


3 21
7 7
1

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

21 = 31×71

Prime Factorization of 33


3 33
11 11
1

Prime factors of 33 are 3,11. Prime factorization of 33 in exponential form is:

33 = 31×111

Now multiplying the highest exponent prime factors to calculate the LCM of 21 and 33.

LCM(21,33) = 31×71×111
LCM(21,33) = 231

Factors of 21

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

1, 3, 7, 21

Factors of 33

List of positive integer factors of 33 that divides 33 without a remainder.

1, 3, 11, 33

Least Common Multiple of 21 and 33 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21 and 33, than apply into the LCM equation.

GCF(21,33) = 3
LCM(21,33) = ( 21 × 33) / 3
LCM(21,33) = 693 / 3
LCM(21,33) = 231

Properties of LCM 21 and 33

(i) The LCM of 33 and 21 is associative

LCM of 21 and 33 = LCM of 33 and 21

Related Least Common Multiples of 21

Related Least Common Multiples of 33

Frequently Asked Questions on LCM of 21 and 33

1. What is the LCM of 21 and 33?

Answer: LCM of 21 and 33 is 231.

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 33?

Answer: Factors of 33 are 1, 3, 11, 33. There are 4 integers that are factors of 33. The greatest factor of 33 is 33.

4. How to Find the LCM of 21 and 33?

Answer:

Least Common Multiple of 21 and 33 = 231

Step 1: Find the prime factorization of 21

21 = 3 x 7

Step 2: Find the prime factorization of 33

33 = 3 x 11

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

LCM = 231 = 3 x 7 x 11

Step 4: Therefore, the least common multiple of 21 and 33 is 231.