Least Common Multiple of 2 and 21

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

• Least Common Multiple of 2 and 21 by Prime method
• Least Common Multiple of 2 and 21 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 2 and 21. First we will calculate the prime factors of 2 and 21.

Prime Factorization of 2

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

2 = 2¹

Prime Factorization of 21

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

21 = 3¹×7¹

Now multiplying the highest exponent prime factors to calculate the LCM of 2 and 21.

LCM(2,21) = 2¹×3¹×7¹
LCM(2,21) = 42

Factors of 2

List of positive integer factors of 2 that divides 2 without a remainder.

1, 2

Factors of 21

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

1, 3, 7, 21

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2 and 21, than apply into the LCM equation.

GCF(2,21) = 1
LCM(2,21) = ( 2 × 21) / 1
LCM(2,21) = 42 / 1
LCM(2,21) = 42

(i) The LCM of 21 and 2 is associative

LCM of 2 and 21 = LCM of 21 and 2

1. What is the LCM of 2 and 21?

Answer: LCM of 2 and 21 is 42.

2. What are the Factors of 2?

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

3. 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.

4. How to Find the LCM of 2 and 21?

Answer:

Least Common Multiple of 2 and 21 = 42

Step 1: Find the prime factorization of 2

2 = 2

Step 2: Find the prime factorization of 21

21 = 3 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 = 42 = 2 x 3 x 7

Step 4: Therefore, the least common multiple of 2 and 21 is 42.