Least Common Multiple of 5 and 21

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

• Least Common Multiple of 5 and 21 by Prime method
• Least Common Multiple of 5 and 21 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 5 and 21. First we will calculate the prime factors of 5 and 21.

Prime Factorization of 5

Prime factors of 5 are 5. Prime factorization of 5 in exponential form is:

5 = 5¹

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 5 and 21.

LCM(5,21) = 3¹×5¹×7¹
LCM(5,21) = 105

Factors of 5

List of positive integer factors of 5 that divides 5 without a remainder.

1, 5

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 5 and 21, than apply into the LCM equation.

GCF(5,21) = 1
LCM(5,21) = ( 5 × 21) / 1
LCM(5,21) = 105 / 1
LCM(5,21) = 105

(i) The LCM of 21 and 5 is associative

LCM of 5 and 21 = LCM of 21 and 5

1. What is the LCM of 5 and 21?

Answer: LCM of 5 and 21 is 105.

2. What are the Factors of 5?

Answer: Factors of 5 are 1, 5. There are 2 integers that are factors of 5. The greatest factor of 5 is 5.

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 5 and 21?

Answer:

Least Common Multiple of 5 and 21 = 105

Step 1: Find the prime factorization of 5

5 = 5

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 = 105 = 3 x 5 x 7

Step 4: Therefore, the least common multiple of 5 and 21 is 105.