Least Common Multiple of 15 and 21

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

• Least Common Multiple of 15 and 21 by Prime method
• Least Common Multiple of 15 and 21 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 15 and 21. First we will calculate the prime factors of 15 and 21.

Prime Factorization of 15

Prime factors of 15 are 3,5. Prime factorization of 15 in exponential form is:

15 = 3¹×5¹

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 15 and 21.

LCM(15,21) = 3¹×5¹×7¹
LCM(15,21) = 105

Factors of 15

List of positive integer factors of 15 that divides 15 without a remainder.

1, 3, 5, 15

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 15 and 21, than apply into the LCM equation.

GCF(15,21) = 3
LCM(15,21) = ( 15 × 21) / 3
LCM(15,21) = 315 / 3
LCM(15,21) = 105

(i) The LCM of 21 and 15 is associative

LCM of 15 and 21 = LCM of 21 and 15

1. What is the LCM of 15 and 21?

Answer: LCM of 15 and 21 is 105.

2. What are the Factors of 15?

Answer: Factors of 15 are 1, 3, 5, 15. There are 4 integers that are factors of 15. The greatest factor of 15 is 15.

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 15 and 21?

Answer:

Least Common Multiple of 15 and 21 = 105

Step 1: Find the prime factorization of 15

15 = 3 x 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 15 and 21 is 105.